topic entry on axioms and foundations of homology and cohomology theories
1 Axioms for Homology and Cohomology theories
- 1.
Axioms for homology
theory and uniqueness theorems
- 2.
Cech types
- 3.
-theory
- 4.
Generalized cohomology
- 5.
Generalized (extraordinary) homology and cohomology
theories
- 6.
Galois Cohomology and Categorical Galois theories
- 7.
(Co)homology of commutative rings and algebras (e.g., Hochschild, André–Quillen, cyclic, dihedral, etc.)
- 8.
Bordism
and cobordism theories, formal group laws
- 9.
Homology with local coefficients, equivariant cohomology
- 10.
Sheaf cohomology
- 11.
Cohomology in Noncommutative algebraic geometry
- 12.
Classifying spaces
for foliations; Gelfand-Fuks cohomology
- 13.
Intersection homology and cohomology
- 14.
Elliptic cohomology
- 15.
Equivariant homology and cohomology
- 16.
Homology and homotopy
of topological groups
and related structures
- 17.
Homotopy Quantum Field Theories and Axiomatic Quantum Field Theories
- 18.
Non-Abelian
Homological Algebra
- 19.
Grothendieck’s ‘Anabelian Geometry’
- 20.
Other homology theories–Your new additions
References
- 1 Hatcher, A. 2001. http://www.math.cornell.edu/ hatcher/AT/AT.pdfAlgebraic Topology (textbook on line)., Cambridge University Press; Cambridge, UK., 405 pages.
- 2 Ronald Brown: Topology and Groupoids, BookSurge LLC (2006).
- 3 Ronald Brown R, P.J. Higgins, and R. Sivera.: “Non-Abelian algebraic topology”, (2008).
- 4 R. Brown and J.-L. Loday: Homotopical excision, and Hurewicz theorems, for n-cubes of spaces, Proc. London Math. Soc., 54:(3), 176-192, (1987).
- 5 R. Brown and J.-L. Loday: Van Kampen Theorems
for diagrams of spaces, Topology, 26: 311-337 (1987).
- 6 R. Brown and C.B. Spencer: Double groupoids
and crossed modules, Cahiers Top. Géom. Diff., 17 (1976), 343-362.
- 7 Allain Connes: Noncommutative Geometry, Academic Press 1994.
- 8 May, J.P. 1999, A Concise Course in Algebraic Topology., The University of Chicago Press: Chicago