Relevant bibliographies by topics / Algebraic topology – Homology and cohomology theories – Sheaf cohomology

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Algebraic topology – Homology and cohomology theories – Sheaf cohomology'

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

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Journal articles on the topic "Algebraic topology – Homology and cohomology theories – Sheaf cohomology"

1

GILLAM, WILLIAM D. "A SHEAF-THEORETIC DESCRIPTION OF KHOVANOV'S KNOT HOMOLOGY." Journal of Knot Theory and Its Ramifications 21, no. 05 (2012): 1250053. http://dx.doi.org/10.1142/s0218216511010061.

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We give a description of Khovanov's knot homology theory in the language of sheaves. To do this, we identify two cohomology theories associated to a commutative diagram of abelian groups indexed by elements of the cube {0, 1}n. The first is obtained by taking the cohomology groups of the chain complex constructed by summing along the diagonals of the cube and inserting signs to force d2 = 0. The second is obtained by regarding the commutative diagram as a sheaf on the cube (in the order-filter topology) and considering sheaf cohomology with supports. Included is a general study of sheaves on f
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2

Pascual-Gainza, Pere. "On the simple object associated to a diagram in a closed model category." Mathematical Proceedings of the Cambridge Philosophical Society 100, no. 3 (1986): 459–74. http://dx.doi.org/10.1017/s0305004100066202.

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In this paper we develop a descent technique for generalized (co)-homology theories defined in the category of algebraic varieties. By such a theory we mean a functor Sch→C, where C is a closed model category in the sense of Quillen satisfying certain axioms (cf. §4). We have chosen to work in such a general context so as to include two situations for which the results of SGA 4 of Deligne and Saint-Donat are not applicable: descent of multiplicative structures (i.e. of differential graded algebras) and descent for generalized sheaf cohomology (such as the algebraic K-theory of coherent sheaves
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Isaksen, Daniel C., and Armira Shkembi. "Motivic connective K-theories and the cohomology of A(1)." Journal of K-theory 7, no. 3 (2011): 619–61. http://dx.doi.org/10.1017/is011004009jkt154.

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AbstractWe make some computations in stable motivic homotopy theory over Spec ℂ, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct over ℂ a motivic analogue of the real K-theory spectrum KO. We also establish a theory of motivic connective covers over ℂ to obtain a motivic version of ko. We establish an Adams spectral sequence for computing motivic ko-homology. The E2-term of this spectral sequence involves Ext groups over the subalgebra A(1) of the motivic Steenrod algebra. We make several explicit computations of these E2-terms in interesting speci
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NEHANIV, CHRYSTOPHER LEV. "ALGEBRAIC CONNECTIVITY." International Journal of Algebra and Computation 01, no. 04 (1991): 445–71. http://dx.doi.org/10.1142/s0218196791000316.

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Let [Formula: see text] be a type of algebra in the sense of universal algebra. By defining singular simplices in algebras and emulating singular [co] homology, we introduce for each variety, pseudo-variety, and divisional class V of type [Formula: see text], a homology and cohomology theory which measure the V-connectivity of type-[Formula: see text] algebras. Intuitively, if we were to think of an algebra as a space and subalgebras which lie in V as simplices, then V-connectivity describes the failure of subalgebras to lie in V, i.e., it describes the "holes" in this space. These [co]homolog
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Dissertations / Theses on the topic "Algebraic topology – Homology and cohomology theories – Sheaf cohomology"

1

Krempasky, Seyide Denise. "Symmetric Squaring in Homology and Bordism." Doctoral thesis, 2011. http://hdl.handle.net/11858/00-1735-0000-0006-B3F0-3.

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Betrachtet man das kartesische Produkt X × X eines topologischen Raumes X mit sich selbst, so kann auf diesem Objekt insbesondere die Involution betrachtet werden, die die Koordinaten vertauscht, die also (x,y) auf (y,x) abbildet. Das sogenannte 'Symmetrische Quadrieren' in Čech-Homologie mit Z/2-coefficients wurde von Schick et al. 2007 als Abbildung von der k-ten Čech-Homologiegruppe eines Raumes X in die 2k-te Čech-Homologiegruppe von X × X modulu der oben genannten Involution definiert. Es st
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Books on the topic "Algebraic topology – Homology and cohomology theories – Sheaf cohomology"

1

1974-, Zomorodian Afra J., ed. Advances in applied and computational topology: American Mathematical Society Short Course on Computational Topology, January 4-5, 2011, New Orleans, Louisiana. American Mathematical Society, 2012.

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Topological modular forms. American Mathematical Society, 2014.

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1975-, Panov Taras E., ed. Toric topology. American Mathematical Society, 2015.

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Modern classical homotopy theory. American Mathematical Society, 2011.

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Ausoni, Christian, 1968- editor of compilation, Hess, Kathryn, 1967- editor of compilation, Johnson Brenda 1963-, Lück, Wolfgang, 1957- editor of compilation, and Scherer, Jérôme, 1969- editor of compilation, eds. An Alpine expedition through algebraic topology: Fourth Arolla Conference, algebraic topology, August 20-25, 2012, Arolla, Switzerland. American Mathematical Society, 2014.

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Stanford Symposium on Algebraic Topology: Applications and New Directions (2012 : Stanford, Calif.), ed. Algebraic topology: Applications and new directions : Stanford Symposium on Algebraic Topology: Applications and New Directions, July 23--27, 2012, Stanford University, Stanford, CA. American Mathematical Society, 2014.

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Basterra, Maria, Kristine Bauer, Kathryn Hess, and Brenda Johnson. Women in topology: Collaborations in homotopy theory : WIT, Women in Topology Workshop, August 18-23, 2013, Banff International Research Station, Banff, Alberta, Canada. American Mathematical Society, 2015.

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Conference Board of the Mathematical Sciences and NSF-CBMS Regional Conference in the Mathematical Sciences on Deformation Theory of Algebras and Modules (2011 : Raleigh, N.C.), eds. Deformation theory of algebras and their diagrams. Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2012.

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Roe, John. Winding around: The winding number in topology, geometry, and analysis. American Mathematical Society, 2015.

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Center for Mathematics at Notre Dame and American Mathematical Society, eds. Toplogy and field theories: Center for Mathematics at Notre Dame, Center for Mathematics at Notre Dame : summer school and conference, Topology and field theories, May 29-June 8, 2012, University of Notre Dame, Notre Dame, Indiana. American Mathematical Society, 2014.

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Book chapters on the topic "Algebraic topology – Homology and cohomology theories – Sheaf cohomology"

1

Switzer, Robert M. "Homology and Cohomology Theories." In Algebraic Topology — Homotopy and Homology. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-61923-6_8.

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Dodson, C. T. J., and Phillip E. Parker. "Homology and Cohomology Theories." In A User’s Guide to Algebraic Topology. Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-6309-9_5.

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Adhikari, Mahima Ranjan. "Homology and Cohomology Theories." In Basic Algebraic Topology and its Applications. Springer India, 2016. http://dx.doi.org/10.1007/978-81-322-2843-1_10.

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Adhikari, Mahima Ranjan. "Spectral Homology and Cohomology Theories." In Basic Algebraic Topology and its Applications. Springer India, 2016. http://dx.doi.org/10.1007/978-81-322-2843-1_15.

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Dieudonné, Jean. "The Various Homology and Cohomology Theories." In A History of Algebraic and Differential Topology, 1900 - 1960. Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4907-4_5.

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Adhikari, Mahima Ranjan. "Eilenberg–Steenrod Axioms for Homology and Cohomology Theories." In Basic Algebraic Topology and its Applications. Springer India, 2016. http://dx.doi.org/10.1007/978-81-322-2843-1_12.

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