topic entry on axioms and foundations of homology and cohomology theories


1 Axioms for Homology and Cohomology theories

  1. 1.

    Axioms for homologyMathworldPlanetmathPlanetmath theory and uniqueness theorems

  2. 2.

    Cech types

  3. 3.

    K-theory

  4. 4.

    Generalized cohomology

  5. 5.

    Generalized (extraordinary) homology and cohomologyMathworldPlanetmath theories

  6. 6.

    Galois Cohomology and Categorical Galois theories

  7. 7.

    (Co)homology of commutative rings and algebras (e.g., Hochschild, André–Quillen, cyclic, dihedral, etc.)

  8. 8.

    BordismMathworldPlanetmath and cobordism theories, formal group laws

  9. 9.

    Homology with local coefficients, equivariant cohomology

  10. 10.
  11. 11.

    Cohomology in Noncommutative algebraic geometry

  12. 12.

    Classifying spacesPlanetmathPlanetmath for foliations; Gelfand-Fuks cohomology

  13. 13.

    Intersection homology and cohomology

  14. 14.

    Elliptic cohomology

  15. 15.

    Equivariant homology and cohomology

  16. 16.

    Homology and homotopyMathworldPlanetmath of topological groupsMathworldPlanetmath and related structures

  17. 17.

    Homotopy Quantum Field Theories and Axiomatic Quantum Field Theories

  18. 18.

    Non-AbelianPlanetmathPlanetmath Homological Algebra

  19. 19.

    Grothendieck’s ‘Anabelian Geometry’

  20. 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 TheoremsMathworldPlanetmath for diagrams of spaces, Topology, 26: 311-337 (1987).
  • 6 R. Brown and C.B. Spencer: Double groupoidsPlanetmathPlanetmathPlanetmath 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
Title topic entry on axioms and foundations of homology and cohomology theories
Canonical name TopicEntryOnAxiomsAndFoundationsOfHomologyAndCohomologyTheories
Date of creation 2013-03-22 18:20:43
Last modified on 2013-03-22 18:20:43
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 12
Author bci1 (20947)
Entry type Topic
Classification msc 11E72
Classification msc 55N99
Classification msc 55N25
Classification msc 55N30
Classification msc 55N05
Classification msc 12G05
Classification msc 14A22
Classification msc 11R34
Classification msc 55N40
Synonym fundamentals of homology and cohomology theories