PlanetPhysics/Topic on Axioms and Foundations of Homology and Cohomology Theories

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Axioms for Homology and Cohomology theories

  1. Axioms for [[../CubicalHigherHomotopyGroupoid/|homology theory]] and uniqueness [[../Formula/|theorems]] #Cech [[../Bijective/|types]] #K-theory
  2. Generalized cohomology
  3. Generalized (extraordinary) homology and [[../NoncommutativeGeometry4/|cohomology theories]]
  4. Galois Cohomology and Categorical Galois theories
  5. (Co)homology of [[../PAdicMeasure/|commutative rings]] and algebras (e.g., Hochschild, Andr\'e-Quillen, cyclic, dihedral, etc.)
  6. Bordism and cobordism theories, formal [[../TrivialGroupoid/|group]] laws
  7. Homology with local coefficients, equivariant cohomology
  8. Sheaf cohomology
  9. Cohomology in [[../AbelianCategory3/|noncommutative]] [[../CoIntersections/|algebraic]] geometry
  10. Classifying spaces for foliations; Gelfand-Fuks cohomology
  11. Intersection homology and cohomology
  12. Elliptic cohomology
  13. Equivariant homology and cohomology
  14. Homology and [[../ThinEquivalence/|homotopy]] of [[../PolishGroup/|topological groups]] and related structures
  15. Homotopy [[../SpaceTimeQuantizationInQuantumGravityTheories/|quantum field theories]] and Axiomatic Quantum Field Theories
  16. [[../AbelianCategory3/|non-Abelian]] Homological Algebra
  17. Grothendieck's `[[../IsomorphismClass/|Anabelian Geometry]]' #Other homology theories--Your new additions

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  1. ↑ Hatcher, A. 2001. Algebraic 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. G\'eom. 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
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