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- Cohomology abstract "In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain complex. That is, cohomology is defined as the abstract study of cochains, cocycles, and coboundaries. Cohomology can be viewed as a method of assigning algebraic invariants to a topological space that has a more refined algebraic structure than does homology. Cohomology arises from the algebraic dualization of the construction of homology. In less abstract language, cochains in the fundamental sense should assign 'quantities' to the chains of homology theory.From its beginning in topology, this idea became a dominant method in the mathematics of the second half of the twentieth century; from the initial idea of homology as a topologically invariant relation on chains, the range of applications of homology and cohomology theories has spread out over geometry and abstract algebra. The terminology tends to mask the fact that in many applications cohomology, a contravariant theory, is more natural than homology. At a basic level this has to do with functions and pullbacks in geometric situations: given spaces X and Y, and some kind of function F on Y, for any mapping f : X → Y composition with f gives rise to a function F o f on X. Cohomology groups often also have a natural product, the cup product, which gives them a ring structure. Because of this feature, cohomology is a stronger invariant than homology, as it can differentiate between certain algebraic objects that homology cannot.".
- Cohomology wikiPageExternalLink ATpage.html.
- Cohomology wikiPageID "194060".
- Cohomology wikiPageLength "13238".
- Cohomology wikiPageOutDegree "131".
- Cohomology wikiPageRevisionID "648053999".
- Cohomology wikiPageWikiLink Abelian_group.
- Cohomology wikiPageWikiLink Abstract_algebra.
- Cohomology wikiPageWikiLink Alexander_duality.
- Cohomology wikiPageWikiLink Alexander–Spanier_cohomology.
- Cohomology wikiPageWikiLink Algebraic_invariant.
- Cohomology wikiPageWikiLink Algebraic_structure.
- Cohomology wikiPageWikiLink Algebraic_topology.
- Cohomology wikiPageWikiLink Allen_Hatcher.
- Cohomology wikiPageWikiLink Andrey_Kolmogorov.
- Cohomology wikiPageWikiLink André–Quillen_cohomology.
- Cohomology wikiPageWikiLink BRST_cohomology.
- Cohomology wikiPageWikiLink BRST_quantization.
- Cohomology wikiPageWikiLink Bonar–Claven_cohomology.
- Cohomology wikiPageWikiLink Bounded_cohomology.
- Cohomology wikiPageWikiLink Brown_representability_theorem.
- Cohomology wikiPageWikiLink Browns_representability_theorem.
- Cohomology wikiPageWikiLink Brown–Peterson_cohomology.
- Cohomology wikiPageWikiLink CW_complex.
- Cohomology wikiPageWikiLink Cap_product.
- Cohomology wikiPageWikiLink Category:Cohomology_theories.
- Cohomology wikiPageWikiLink Category_(mathematics).
- Cohomology wikiPageWikiLink Chain_(algebraic_topology).
- Cohomology wikiPageWikiLink Chain_complex.
- Cohomology wikiPageWikiLink Character_(mathematics).
- Cohomology wikiPageWikiLink Cobordism.
- Cohomology wikiPageWikiLink Coboundary.
- Cohomology wikiPageWikiLink Coherent_cohomology.
- Cohomology wikiPageWikiLink Coherent_sheaf.
- Cohomology wikiPageWikiLink Cohomology.
- Cohomology wikiPageWikiLink Complex_cobordism.
- Cohomology wikiPageWikiLink Continuous_function.
- Cohomology wikiPageWikiLink Covariance_and_contravariance_of_functors.
- Cohomology wikiPageWikiLink Crystalline_cohomology.
- Cohomology wikiPageWikiLink Cup_product.
- Cohomology wikiPageWikiLink Cyclic_cohomology.
- Cohomology wikiPageWikiLink Cyclic_homology.
- Cohomology wikiPageWikiLink Daniel_Quillen.
- Cohomology wikiPageWikiLink De_Rham_cohomology.
- Cohomology wikiPageWikiLink De_Rhams_theorem.
- Cohomology wikiPageWikiLink Deligne_cohomology.
- Cohomology wikiPageWikiLink Diagonal.
- Cohomology wikiPageWikiLink Differential_form.
- Cohomology wikiPageWikiLink Dimension.
- Cohomology wikiPageWikiLink Dirac_cohomology.
- Cohomology wikiPageWikiLink Dual_space.
- Cohomology wikiPageWikiLink Eduard_Čech.
- Cohomology wikiPageWikiLink Edwin_Spanier.
- Cohomology wikiPageWikiLink Eilenberg–Steenrod_axioms.
- Cohomology wikiPageWikiLink Elliptic_cohomology.
- Cohomology wikiPageWikiLink Flat_cohomology.
- Cohomology wikiPageWikiLink Flat_topology.
- Cohomology wikiPageWikiLink Formal_group.
- Cohomology wikiPageWikiLink Foundations_of_Algebraic_Topology.
- Cohomology wikiPageWikiLink Function_(mathematics).
- Cohomology wikiPageWikiLink Functor.
- Cohomology wikiPageWikiLink Galois_cohomology.
- Cohomology wikiPageWikiLink Gelfandxe2x80x93Fuks_cohomology.
- Cohomology wikiPageWikiLink General_position.
- Cohomology wikiPageWikiLink Geometry.
- Cohomology wikiPageWikiLink Georges_de_Rham.
- Cohomology wikiPageWikiLink Graded_ring.
- Cohomology wikiPageWikiLink Group_(mathematics).
- Cohomology wikiPageWikiLink Group_cohomology.
- Cohomology wikiPageWikiLink Harrison_cohomology.
- Cohomology wikiPageWikiLink Hassler_Whitney.
- Cohomology wikiPageWikiLink Henri_Poincaré.
- Cohomology wikiPageWikiLink Hochschild_cohomology.
- Cohomology wikiPageWikiLink Hochschild_homology.
- Cohomology wikiPageWikiLink Homological_algebra.
- Cohomology wikiPageWikiLink Homology_(mathematics).
- Cohomology wikiPageWikiLink Homology_theory.
- Cohomology wikiPageWikiLink Homomorphism.
- Cohomology wikiPageWikiLink Intersection_cohomology.
- Cohomology wikiPageWikiLink Intersection_homology.
- Cohomology wikiPageWikiLink Intersection_theory.
- Cohomology wikiPageWikiLink Invariant_theory.
- Cohomology wikiPageWikiLink James_Waddell_Alexander_II.
- Cohomology wikiPageWikiLink K-theory.
- Cohomology wikiPageWikiLink Khovanov_homology.
- Cohomology wikiPageWikiLink Lev_Pontryagin.
- Cohomology wikiPageWikiLink Lie_algebra_cohomology.
- Cohomology wikiPageWikiLink List_of_cohomology_theories.
- Cohomology wikiPageWikiLink Local_cohomology.
- Cohomology wikiPageWikiLink Manifold.
- Cohomology wikiPageWikiLink Map_(mathematics).
- Cohomology wikiPageWikiLink Mathematics.
- Cohomology wikiPageWikiLink Morava_K-theory.
- Cohomology wikiPageWikiLink Moscow.
- Cohomology wikiPageWikiLink Motivic_cohomology.
- Cohomology wikiPageWikiLink Non-abelian_cohomology.
- Cohomology wikiPageWikiLink Nonabelian_cohomology.
- Cohomology wikiPageWikiLink Norman_Steenrod.
- Cohomology wikiPageWikiLink Perverse_cohomology.
- Cohomology wikiPageWikiLink Poincaré_duality.