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Dissertations / Theses on the topic 'Surgery on manifolds'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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1

Ackermann, Robert James. "Constructing Bitwisted Face Pairing 3-Manifolds." Thesis, Virginia Tech, 2008. http://hdl.handle.net/10919/32655.

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The bitwist construction, originally discovered by Cannon, Floyd, and Parry, gives us a new method for finding face pairing descriptions of 3-manifolds. In this paper, I will describe the construction in a way suitable for a more general audience than the original research papers. Along the way, I will describe Dehn Surgery and a set of moves which allows us to change the framings of a link without changing the topology of the manifold obtained by Dehn Surgery. Once the theory has been developed, I will apply it to find several bitwist representations of the Poincaré Sphere and 3-Torus. Fina
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2

Palmer, Christopher. "Some applications of algebraic surgery theory : 4-manifolds, triangular matrix rings and braids." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/15794.

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This thesis consists of three applications of Ranicki's algebraic theory of surgery to the topology of manifolds. The common theme is a decomposition of a global algebraic object into simple local pieces which models the decomposition of a global topological object into simple local pieces. Part I: Algebraic reconstruction of 4-manifolds. We extend the product and glueing constructions for symmetric Poincaré complexes, pairs and triads to a thickening construction for a symmetric Poincaré representation of a quiver. Gay and Kirby showed that, subject to certain conditions, the fold curves an
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3

Crawford, Thomas. "A Stronger Gordon Conjecture and an Analysis of Free Bicuspid Manifolds with Small Cusps." Thesis, Boston College, 2018. http://hdl.handle.net/2345/bc-ir:107938.

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Thesis advisor: Robert Meyerhoff<br>Thurston showed that for all but a finite number of Dehn Surgeries on a cusped hyperbolic 3-manifold, the resulting manifold admits a hyperbolic structure. Global bounds on this number have been set, and gradually improved upon, by a number of Mathematicians until Lackenby and Meyerhoff proved the sharp bound of 10, which is realized by the figure-eight knot exterior. We improve this result by proving a stronger version of Gordon’s conjecture: that excluding the figure-eight knot exterior, cusped hyperbolic 3-manifolds have at most 8 non-hyperbolic Dehn Surg
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4

Lambert, Lee R. "A Toolkit for the Construction and Understanding of 3-Manifolds." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2188.

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Since our world is experienced locally in three-dimensional space, students of mathematics struggle to visualize and understand objects which do not fit into three-dimensional space. 3-manifolds are locally three-dimensional, but do not fit into 3-dimensional space and can be very complicated. Twist and bitwist are simple constructions that provide an easy path to both creating and understanding closed, orientable 3-manifolds. By starting with simple face pairings on a 3-ball, a myriad of 3-manifolds can be easily constructed. In fact, all closed, connected, orientable 3-manifolds can be devel
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5

Nazaikinskii, Vladimir, Anton Savin, Bert-Wolfgang Schulze, and Boris Sternin. "Differential operators on manifolds with singularities : analysis and topology : Chapter 1: Localization (surgery) in elliptic theory." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2654/.

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Contents: Chapter 1: Localization (Surgery) in Elliptic Theory 1.1. The Index Locality Principle 1.1.1. What is locality? 1.1.2. A pilot example 1.1.3. Collar spaces 1.1.4. Elliptic operators 1.1.5. Surgery and the relative index theorem 1.2. Surgery in Index Theory on Smooth Manifolds 1.2.1. The Booß–Wojciechowski theorem 1.2.2. The Gromov–Lawson theorem 1.3. Surgery for Boundary Value Problems 1.3.1. Notation 1.3.2. General boundary value problems 1.3.3. A model boundary value problem on a cylinder 1.3.4. The Agranovich–Dynin theorem 1.3.5. The Agranovich theorem 1.3.6. Bojarski’s theor
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6

Perlmutter, Nathan. "Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds." Thesis, University of Oregon, 2015. http://hdl.handle.net/1794/19241.

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Let n > 1. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)-dimensional manifolds, with respect to forming the connected sum with (2n-1)-connected, (4n+1)-dimensional manifolds that are stably parallelizable. Our techniques involve the study of the action of the diffeomorphism group of a manifold M on the linking form associated to the homology groups of M. In order to study this action we construct a geometric model for the linking form using the intersections of embedded and immersed Z/k-manifolds. In addition to our main homological sta
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7

Eslami, Rad Anahita. "Effect of Legendrian surgery and an exact sequence for Legendrian links." Doctoral thesis, Universite Libre de Bruxelles, 2012. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209662.

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This thesis is devoted to the study of the effect of Legendrian surgery on contact manifolds. In particular, we study the effect of this surgery on the Reeb dynamics of the contact manifold on which we perform such a surgery along Legendrian links. We obtain an exact sequence of cyclic Legendrian homology for the Legendrian links. Then we present the applications in 3-dimension and higher dimensions.<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished
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8

Krishna, Siddhi. "Taut foliations, positive braids, and the L-space conjecture:." Thesis, Boston College, 2020. http://hdl.handle.net/2345/bc-ir:108731.

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Thesis advisor: Joshua E. Greene<br>We construct taut foliations in every closed 3-manifold obtained by r-framed Dehn surgery along a positive 3-braid knot K in S^3, where r &lt; 2g(K)-1 and g(K) denotes the Seifert genus of K. This confirms a prediction of the L--space conjecture. For instance, we produce taut foliations in every non-L-space obtained by surgery along the pretzel knot P(-2,3,7), and indeed along every pretzel knot P(-2,3,q), for q a positive odd integer. This is the first construction of taut foliations for every non-L-space obtained by surgery along an infinite family of hype
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9

Easson, Vivien R. "Surfaces and subgroups in surgered 3-manifolds." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.434866.

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10

Nazaikinskii, Vladimir, and Boris Sternin. "On surgery in elliptic theory." Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2587/.

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We prove a general theorem on the behavior of the relative index under surgery for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions), this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities.
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11

Nazaikinskii, Vladimir E., and Boris Yu Sternin. "Surgery and the relative index in elliptic theory." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2553/.

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We prove a general theorem on the local property of the relative index for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions) this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities as well as for elliptic bou
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12

Nazaikinskii, Vladimir, Bert-Wolfgang Schulze, and Boris Sternin. "Localization problem in index theory of elliptic operators." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2617/.

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This is a survey of recent results concerning the general index locality principle, associated surgery, and their applications to elliptic operators on smooth manifolds and manifolds with singularities as well as boundary value problems. The full version of the paper is submitted for publication in Russian Mathematical Surveys.
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13

Gerges, Amir. "Surgery, bordism and equivalence of 3-manifolds." Thesis, 1997. http://hdl.handle.net/1911/19161.

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We call two closed, oriented 3-manifolds, $M\sb0$ and $M\sb1,$ HTS-equivalent if there exists a sequence $M\sb{j\sb{i}},\ i = 1..m$ where $M\sb0 = M\sb{j\sb1}$ and $M\sb1 = M\sb{j\sb{m}}$ and $M\sb{j\sb{i}}$ is obtained from $M\sb{j\sb{i-1}}$ by performing $1/k\sb{i}$ Dehn surgery $(k\sb{i}\in\doubz)$ on a knot which is homologically trivial in $H\sb1 (M\sb{j\sb{i-1}}).$ The object of this work is to further characterize this equivalence relation. We show that saying that (i) $M\sb0$ and $M\sb1$ are HTS-equivalent, is equivalent to saying that (ii) $\exists f\sb1:M\sb1\to K(H\sb1(M\sb0),1)$ wh
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14

Dunfield, Nathan M. "Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds /." 1999. http://wwwlib.umi.com/dissertations/fullcit/9934045.

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15

Pederzani, Niccolò. "On the spin cobordism invariance of the homotopy type of the space R^inv(M)." 2018. https://ul.qucosa.de/id/qucosa%3A21391.

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In this PhD thesis we investigate the space R^inv(M): the space of riemannian metrics on a spin manifold M whose associated Dirac operator is invertible. In particular we are interest in the bond between the topology of R^inv(M) and the topology of the underlying manifold M. We conjecture that the homotopy type of R^inv(M) is invariant under spin cobordism.
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16

Ling-Yi, Hsu. "Surgery on Manifold with Positive Scalar Curvature." 2005. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0002-3006200515581300.

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17

Hsu, Ling-Yi, and 許鈴宜. "Surgery on Manifold with Positive Scalar Curvature." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/01616870245192441840.

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碩士<br>淡江大學<br>數學學系碩士班<br>93<br>In this thesis, we study the 0-surgery on a manifold M of dimension . The main theorem can be stated in the following way. If obtained from a Riemannian manifold M with positive scalar curvature, ,by performing 0-surgery can still have a metric with positive scalar curvature. The main technique we use is to construct a neck according to a given curve in the way that X has Riemannian metric on M in the beginning and product metric of the form in the end. We using the Gauss formula to simplify the relation of sectional curvature between X and . Then we als
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18

Bowman, Richard Sean. "Knots in handlebodies with handlebody surgeries." Thesis, 2012. http://hdl.handle.net/2152/ETD-UT-2012-05-5600.

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