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Data publikacji: 4 czerwca 2021

Data aktualizacji: 25 lipca 2025

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1

Gritschacher, Simon. "Commutative K-theory." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:5d5b0e20-20ef-4eec-a032-8bcb5fe59884.

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The bar construction BG of a topological group G has a subcomplex B<sub>com</sub>G ⊂ BG assembled from spaces of commuting elements in G. If G = U;O (the infinite unitary / orthogonal groups) then B<sub>com</sub>U and B<sub>com</sub>O are E<sub>∞</sub>-ring spaces. The corresponding cohomology theory is called commutative K-theory. In this work we study properties of the spaces B<sub>com</sub>G and of infinite loop spaces built from them, with an emphasis on the cases G = U,O. The content of this thesis is organised as follows: In Chapter 1 we consider a family of self-maps of B<sub>

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2

Levikov, Filipp. "L-theory, K-theory and involutions." Thesis, University of Aberdeen, 2013. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=201918.

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In Part 1, we consider two descriptions of L-homology of a (polyhedron of a) simplicial complex X. The classical approach of Ranicki via (Z,X)-modules (cf. [Ran92]) iswell established and is used in Ranicki’s definition of the total surgery obstruction and his formulation of the algebraic surgery exact sequence (cf. [Ran79], [Ran92],[KMM]). This connection between algebraic surgery and geometric surgery has numerous applications in the theory of (highdimensional) manifolds. The approach described in [RW10] uses a category of homotopy complexes of cosheaves to construct for a manifold M a (rati

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3

Takeda, Yuichiro. "Localization theorem in equivariant algebraic K-theory." 京都大学 (Kyoto University), 1997. http://hdl.handle.net/2433/202419.

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4

Stefański, Bogdan. "String theory, dirichlet branes and K-theory." Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621023.

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5

Braun, Volker Friedrich. "K-theory and exceptional holonomy in string theory." Doctoral thesis, [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=965401650.

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6

Mitchener, Paul David. "K-theory of C*-categories." Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365771.

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7

Zakharevich, Inna (Inna Ilana). "Scissors congruence and K-theory." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/73376.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 83-84).<br>In this thesis we develop a version of classical scissors congruence theory from the perspective of algebraic K-theory. Classically, two polytopes in a manifold X are defined to be scissors congruent if they can be decomposed into finite sets of pairwise-congruent polytopes. We generalize this notion to an abstract problem: given a set of objects and decomposition and congruence relations between them, when are two ob

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8

Cain, Christopher. "K-theory of Fermat curves." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/262483.

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I investigate the K_2 groups of the quotients of Fermat curves given in projective coordinates by the equation F_n:X^n+Y^n=Z^n. On any quotient where the number of known elements is equal to the rank predicted by Beilinson’s Conjecture I verify numerically that the determinant of the matrix of regulator values agrees with the leading coefficient of the L-function up to a simple rational number. The main source of K_2 elements are the so-called “symbols with divisorial support at infinity” that were found by Ross in the 1990’s. These consist of symbols of the form f, g where f and g have diviso

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9

Bunch, Eric. "K-Theory in categorical geometry." Diss., Kansas State University, 2015. http://hdl.handle.net/2097/20350.

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Doctor of Philosophy<br>Department of Mathematics<br>Zongzhu Lin<br>In the endeavor to study noncommutative algebraic geometry, Alex Rosenberg defined in [13] the spectrum of an Abelian category. This spectrum generalizes the prime spectrum of a commutative ring in the sense that the spectrum of the Abelian category R − mod is homeomorphic to the prime spectrum of R. This spectrum can be seen as the beginning of “categorical geometry”, and was used in [15] to study noncommutative algebriac geometry. In this thesis, we are concerned with geometries extending beyond traditional algebraic g

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10

Hedlund, William. "K-Theory and An-Spaces." Thesis, Uppsala universitet, Algebra och geometri, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-414082.

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11

Hahn, Rebekah D. "K(1)-local Iwasawa theory /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/5736.

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12

Millar, Judith Ruth. "K-theory of Azumaya algebras." Thesis, Queen's University Belfast, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.534610.

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13

Niwa, Masahiko. "THEORY OF G-CATEGORIES TOWARD EQUIVARIANT ALGEBRAIC K-THEORY." 京都大学 (Kyoto University), 1991. http://hdl.handle.net/2433/168801.

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本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものである<br>Kyoto University (京都大学)<br>0048<br>新制・論文博士<br>理学博士<br>乙第7383号<br>論理博第1122号<br>新制||理||718(附属図書館)<br>UT51-91-C116<br>(主査)教授戸田宏, 教授土方弘明, 教授丸山正樹<br>学位規則第5条第2項該当

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14

Schäfer-Nameki, Sakura. "D-branes in boundary field theory and K-theory." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620017.

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15

Piazza, Paolo. "K-theory and index theory on manifolds with boundary." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/31020.

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16

Zhang, Zuhong. "Lower K-theory of unitary groups." Thesis, Queen's University Belfast, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486261.

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The study of the sandwich classification theorem of unitary hyperbolic groups over commutative form ring (R, A) (in the sense of Bak) is naturally inspired by the sandwich classification theorem of general linear groups, which is initialed by Bak in a manuscript in 1967. In Chapter 1, we briefly review the history of the developing of normal and subnormal structure problems in the setting of general linear group and unitary group, as well as the co~nectionwith other problems. The proofs of sandwich. classification theorem and the structure theorem of subnormal subgroups of general linear group

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17

Kerz, Moritz. "Milnor K-theory of local rings." kostenfrei, 2008. http://www.opus-bayern.de/uni-regensburg/volltexte/2008/991/.

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18

Clausen, Dustin (Dustin Tate). "Arithmetic duality in algebraic K-theory." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/83692.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Mathematics, 2013.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 37-38).<br>Let X be a regular arithmetic curve or point (meaning a regular separated scheme of finite type over Z which is connected and of Krull dimension </= 1). We define a compactly-supported variant Kc(X) of the algebraic K-theory spectrum K(X), and establish the basic functoriality of Kc. Briefly, K, behaves as if it were dual to K. Then we give this duality some grounding: for every prime t invertible on X, we def

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19

Harris, Thomas. "Binary complexes and algebraic K-theory." Thesis, University of Southampton, 2015. https://eprints.soton.ac.uk/383999/.

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20

Magill, Matthew. "Topological K-theory and Bott Periodicity." Thesis, Uppsala universitet, Algebra och geometri, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-322927.

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21

Sia, Charmaine Jia Min. "Structures on Forms of K-Theory." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:17467390.

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In the early 1970s, Morava studied forms of topological K-theory and observed that they have interesting number theoretic connections. Until very recently, forms of K-theory have not been studied in greater depth and integrated into the modern theory of topological modular forms. In this dissertation, some expected structured ring spectra and locality results are established on forms of K-theory. Forms of algebraic structures are usually classified by Galois cohomology. Based on the structured ring spectra and locality results established, a criterion is given for distinguishing homotopy equiv

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22

Klippenstien, J. "Applications of the universal coefficient theorem for connective k-theory." Thesis, University of Warwick, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.371053.

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23

Hazrat, Roozbeh. "On K-theory of classical-like groups." [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=969899742.

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24

Hekmati, Pedram. "Group Extensions, Gerbes and Twisted K-theory." Licentiate thesis, Stockholm : Teoretisk fysik, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4654.

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25

Lopez, Jose Maria Cantarero. "Equivariant K-theory, groupoids and proper actions." Thesis, University of British Columbia, 2009. http://hdl.handle.net/2429/14707.

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Equivariant K-theory for actions of groupoids is defined and shown to be a cohomology theory on the category of finite equivariant CW-complexes. Under some conditions, these theories are representable. We use this fact to define twisted equivariant K-theory for actions of groupoids. A classification of possible twistings is given. We also prove a completion theorem for twisted and untwisted equivariant K-theory. Finally, some applications to proper actions of Lie groups are discussed.

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26

Yang, Shuhang. "Large N gauge theory and k-strings." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/33648.

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We considered the k-antisymmetric representation of U(N) gauge group on two dimensional lattice space and derived the free energy by saddle point approximation in large N limit. k is a large integer comparable with N. Besides Gross-Witten phase transition[1], which happens as the coupling constant changes, we found a new phase transition in the strong coupling system that happens as k changes. The free energy of the weak coupling system is a smooth function of k under continuous limit. We have carefully selected the right saddle point solution among other possible ones. The numerical results m

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27

Kreisel, Michael. "Gabor frames for quasicrystals and K-theory." Thesis, University of Maryland, College Park, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3711683.

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<p> We study the connection between Gabor frames for quasicrystals, the topology of the hull of a quasicrystal, and the K-theory of an associated twisted groupoid algebra. In particular, we construct a finitely generated projective module over this algebra, and multiwindow Gabor frames can be used to construct an idempotent representing the module in <i>K</i>-theory. For lattice subsets in dimension two, this allows us to prove a twisted version of Bellissard's gap labeling theorem. By viewing Gabor frames in this operator algebraic framework, we are also able to show that for certain quasicry

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28

Lakos, Gyula 1973. "Smooth K-theory and locally convex algebras." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/29357.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.<br>Includes bibliographical references (p. 121-122).<br>In this thesis, we improve the loop linearization process from the classical article of Atiyah and Bott on Bott periodicity. The linearization process is made explicit in terms of formulae for smooth loops. Using this improvement allows us to extend K-theory (including periodicity) to a class of locally convex algebras vastly larger then the one of Banach algebras. We find various ways to represent periodicity by explicit formulae. For finite Laurent loops

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29

Dugger, Daniel (Daniel Keith) 1972. "A Postnikov tower for algebraic K-theory." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/85300.

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30

Song, Yongjin. "Hermitian algebraic K-theory and dihedral homology /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487681788252481.

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31

Savinien, Jean P. X. "Cohomology and K-theory of aperiodic tilings." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24732.

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Thesis (Ph.D.)--Mathematics, Georgia Institute of Technology, 2008.<br>Committee Chair: Prof. Jean Bellissard; Committee Member: Prof. Claude Schochet; Committee Member: Prof. Michael Loss; Committee Member: Prof. Stavros Garoufalidis; Committee Member: Prof. Thang Le.

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32

Rodtes, Kijti. "The connective K theory of semidihedral groups." Thesis, University of Sheffield, 2010. http://etheses.whiterose.ac.uk/1103/.

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The real connective K-homology of finite groups ko¤(BG), plays a big role in the Gromov-Lawson-Rosenberg (GLR) conjecture. In order to compute them, we can calculate complex connective K-cohomology, ku¤(BG), first and then follow by computing complex connective K-homology, ku¤(BG), or by real connective K-cohomology,ko¤(BG). After we apply the eta-Bockstein spectral sequence to ku¤(BG) or the Greenlees spectral sequence to ko¤(BG), we shall get ko¤(BG). In this thesis, we compute all of them algebraically and explicitly to reduce the di±culties of geometric construction for GLR, especially for

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33

Dell'Aiera, Clément. "Controlled K-theory for groupoids and applications." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0114/document.

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Dans leur article de 2015 intitulé "On quantitative operator K-theory", H. Oyono-Oyono et G. Yu introduisent un raffinement de la K-théorie opératorielle adapté au cadre desC*-algèbres filtrées, appelé K-théorie quantitative ou contrôlée. Dans cette thèse, nous généralisons la notion de filtration de C_-algèbres. Nous montrons ensuite que ce cadre contient celui déjà traité par G. Yu et H. Oyono-Oyono, tout en se révélant assez souple pour traiter les produits croisés de groupoïdes étalés et de groupes quantiques discrets. Nous construisons ensuite des applications d'assemblage _a valeurs dans

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34

Dell'Aiera, Clément. "Controlled K-theory for groupoids and applications." Electronic Thesis or Diss., Université de Lorraine, 2017. http://www.theses.fr/2017LORR0114.

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Dans leur article de 2015 intitulé "On quantitative operator K-theory", H. Oyono-Oyono et G. Yu introduisent un raffinement de la K-théorie opératorielle adapté au cadre desC*-algèbres filtrées, appelé K-théorie quantitative ou contrôlée. Dans cette thèse, nous généralisons la notion de filtration de C_-algèbres. Nous montrons ensuite que ce cadre contient celui déjà traité par G. Yu et H. Oyono-Oyono, tout en se révélant assez souple pour traiter les produits croisés de groupoïdes étalés et de groupes quantiques discrets. Nous construisons ensuite des applications d'assemblage _a valeurs dans

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35

Rallis, Nikolaos. "C-K Theory in Practice : C-K Theory in Practice: How can CK Theory serve as a model of reasoning for Startups’ Internationalization?" Thesis, Linköpings universitet, Företagsekonomi, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-160692.

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Background: In the past few decades the world business map has shrunk considerably. Economic unions, tighter cooperation between different countries and across continents is nowadays setting the pace of current economy trends. Moreover, the rise of the internet and technology has interconnected people and markets more than ever. In this dynamic new setting, entrepreneurs and novel ideas have found the ideal ground to flourish. Startups are taking the business world by storm. Moreover, many of them are ambitious enough to engage in International markets right after their conception. It would be

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36

Jia, Bei. "D-branes and K-homology." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/32039.

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In this thesis the close relationship between the topological $K$-homology group of the spacetime manifold $X$ of string theory and D-branes in string theory is examined. An element of the $K$-homology group is given by an equivalence class of $K$-cycles $[M,E,\phi]$, where $M$ is a closed spin$^c$ manifold, $E$ is a complex vector bundle over $M$, and $\phi: M\rightarrow X$ is a continuous map. It is proposed that a $K$-cycle $[M,E,\phi]$ represents a D-brane configuration wrapping the subspace $\phi(M)$. As a consequence, the $K$-homology element defined by $[M,E,\phi]$ represents a class of

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37

Hüttemann, Thomas. "Algebraic K-theory of non-linear projectice spaces." [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=957056230.

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38

Savin, Anton, and Boris Sternin. "Eta-invariant and Pontrjagin duality in K-theory." Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2574/.

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The topological significance of the spectral Atiyah-Patodi-Singer η-invariant is investigated. We show that twice the fractional part of the invariant is computed by the linking pairing in K-theory with the orientation bundle of the manifold. The Pontrjagin duality implies the nondegeneracy of the linking form. An example of a nontrivial fractional part for an even-order operator is presented.

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39

Hignett, Anthony James. "Discrete module categories and operations in K-theory." Thesis, University of Sheffield, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.521994.

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40

Valentino, Alessandro. "K-theory, D-branes and Ramond-Ramond fields." Thesis, Heriot-Watt University, 2008. http://hdl.handle.net/10399/2175.

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This thesis is dedicated to the study of K-theoretical properties of D-branes and Ramond-Ramond fields. We construct abelian groups which define a homology theory on the category CW-complexes, and prove that this homology theory is equivalent to the bordism 3n of KO-homology, the dual theory to KO-theory. We construct an isomorphism between our geometric representation and the SLUdlytic representation of KO-homology, which induces a natural equivalence of homology functors. We apply this framework to describe mathematical properties of D-branes in type I String theory.

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41

Markett, Simon A. "The Grayson spectral sequence for hermitian K-theory." Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/74068/.

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Let R be a regular ring such that 2 is invertible. We construct a spectral sequence converging to the hermitian K-theory, alias the Grothendieck-Witt theory, of R. In particular, we construct a tower for the hermitian K-groups in even shifts, whose terms are given by the hermitian K-theory of automorphisms. The spectral sequence arises as the homotopy spectral sequence of this tower and is analogous to Grayson’s version of the motivic spectral sequence [Gra95]. Further, we construct similar towers for the hermitian K-theory in odd shifts if R is a field of characteristic different from 2. We s

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42

Thiang, Guo Chuan. "Topological phases of matter, symmetries, and K-theory." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:53b10289-8b59-46c2-a0e9-5a5fb77aa2a2.

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This thesis contains a study of topological phases of matter, with a strong emphasis on symmetry as a unifying theme. We take the point of view that the "topology" in many examples of what is loosely termed "topological matter", has its origin in the symmetry data of the system in question. From the fundamental work of Wigner, we know that topology resides not only in the group of symmetries, but also in the cohomological data of projective unitary-antiunitary representations. Furthermore, recent ideas from condensed matter physics highlight the fundamental role of charge-conjugation symmetry.

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43

Schadeck, Laurent. "On the K-theory of tame Artim stacks." Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85745.

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This thesis pertains to the algebraic K-theory of tame Artin stacks. Building on earlier work of Vezzosi and Vistoli in equivariant K-theory, which we translate in stacky language, we give a description of the algebraic K-groups of tame quotient stacks. Using a strategy of Vistoli, we recover Grothendieck-Riemann-Roch-like formulae for tame quotient stacks that refine Toën’s Grothendieck-Riemann-Roch formula for Deligne-Mumford stacks (as it was realized that the latter pertains to quotient stacks since it relies on the resolution property). Our formulae differ from Toën’s in that, instead of

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44

Sperber, Ron. "A comparison of assembly maps in algebraic K-theory." Diss., Online access via UMI:, 2004. http://wwwlib.umi.com/dissertations/fullcit/3150488.

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45

Patronas, Dimitrios [Verfasser]. "The Artin Defect in Algebraic K-Theory / Dimitrios Patronas." Berlin : Freie Universität Berlin, 2014. http://d-nb.info/1058105280/34.

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46

Kolin, David. "k-Space image correlation spectroscopy: theory, verification, and applications." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=21933.

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This thesis is about the use and development of new fluorescence correlation techniques to measure the dynamics, number density, and aggregation state of fluorescently labelled proteins in living cells. An extensive investigation of the accuracy and precision of temporal image correlation spectroscopy (TICS) is presented first. Using computer simulations of laser scanning microscopy image time series, the effect of spatiotemporal sampling, particle density, noise, and photobleaching of fluorophores on the recovery of transport coefficients and number densities by TICS is investigated. It is s

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47

Strong, Mary-Jane Anne. "Additive Unstable Operations in Complex K-Theory and Cobordism." Thesis, University of Westminster, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.500535.

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48

Kuber, Amit Shekhar. "K-theory of theories of modules and algebraic varieties." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/ktheory-of-theories-of-modules-and-algebraic-varieties(5d4387d5-df36-455a-a09d-922d67b0827e).html.

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49

Melo, S. T., R. Nest, and Elmar Schrohe. "C*-structure and K-theory of Boutet de Monvel's algebra." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2616/.

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We consider the norm closure A of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a manifold X with boundary ∂X. We first describe the image and the kernel of the continuous extension of the boundary principal symbol homomorphism to A. If X is connected and ∂X is not empty, we then show that the K-groups of A are topologically determined. In case the manifold, its boundary, and the cotangent space of its interior have torsion free K-theory, we get Ki(A,k) congruent Ki(C(X))⊕Ksub(1-i)(Csub(0)(T*X)),i = 0,1, with k denoting the compact ideal, and T*X denoti

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Narreddy, Naga Sambu Reddy, and Tuğrul Durgun. "Clusters (k) Identification without Triangle Inequality : A newly modelled theory." Thesis, Uppsala universitet, Institutionen för informatik och media, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-183608.

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Cluster analysis characterizes data that are similar enough and useful into meaningful groups (clusters).For example, cluster analysis can be applicable to find group of genes and proteins that are similar, to retrieve information from World Wide Web, and to identify locations that are prone to earthquakes. So the study of clustering has become very important in several fields, which includes psychology and other social sciences, biology, statistics, pattern recognition, information retrieval, machine learning and data mining [1] [2]. Cluster analysis is the one of the widely used technique

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