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- Universal_coefficient_theorem abstract "In algebraic topology, universal coefficient theorems establish relationships between homology and cohomology theories. For instance, the integral homology theory of a topological space X, and its homology with coefficients in any abelian group A are related as follows: the integral homology groupsHi(X; Z)completely determine the groupsHi(X; A)Here Hi might be the simplicial homology or more general singular homology theory: the result itself is a pure piece of homological algebra about chain complexes of free abelian groups. The form of the result is that other coefficients A may be used, at the cost of using a Tor functor. For example it is common to take A to be Z/2Z, so that coefficients are modulo 2. This becomes straightforward in the absence of 2-torsion in the homology. Quite generally, the result indicates the relationship that holds between the Betti numbers bi of X and the Betti numbers bi,F with coefficients in a field F. These can differ, but only when the characteristic of F is a prime number p for which there is some p-torsion in the homology.".
- Universal_coefficient_theorem wikiPageExternalLink ATpage.html.
- Universal_coefficient_theorem wikiPageExternalLink 768481.
- Universal_coefficient_theorem wikiPageID "996107".
- Universal_coefficient_theorem wikiPageLength "6592".
- Universal_coefficient_theorem wikiPageOutDegree "36".
- Universal_coefficient_theorem wikiPageRevisionID "688465772".
- Universal_coefficient_theorem wikiPageWikiLink Abelian_group.
- Universal_coefficient_theorem wikiPageWikiLink Adjoint.
- Universal_coefficient_theorem wikiPageWikiLink Algebraic_topology.
- Universal_coefficient_theorem wikiPageWikiLink Allen_Hatcher.
- Universal_coefficient_theorem wikiPageWikiLink Betti_number.
- Universal_coefficient_theorem wikiPageWikiLink Bockstein_spectral_sequence.
- Universal_coefficient_theorem wikiPageWikiLink Category:Homological_algebra.
- Universal_coefficient_theorem wikiPageWikiLink Category:Theorems_in_algebraic_topology.
- Universal_coefficient_theorem wikiPageWikiLink Chain_complex.
- Universal_coefficient_theorem wikiPageWikiLink Characteristic_(algebra).
- Universal_coefficient_theorem wikiPageWikiLink Closed_manifold.
- Universal_coefficient_theorem wikiPageWikiLink Cohomology.
- Universal_coefficient_theorem wikiPageWikiLink Cohomology_ring.
- Universal_coefficient_theorem wikiPageWikiLink Connected_space.
- Universal_coefficient_theorem wikiPageWikiLink Eilenberg–MacLane_space.
- Universal_coefficient_theorem wikiPageWikiLink Exact_sequence.
- Universal_coefficient_theorem wikiPageWikiLink Ext_functor.
- Universal_coefficient_theorem wikiPageWikiLink Field_(mathematics).
- Universal_coefficient_theorem wikiPageWikiLink Finitely_generated_abelian_group.
- Universal_coefficient_theorem wikiPageWikiLink Free_abelian_group.
- Universal_coefficient_theorem wikiPageWikiLink Functor.
- Universal_coefficient_theorem wikiPageWikiLink Homological_algebra.
- Universal_coefficient_theorem wikiPageWikiLink Homology_(mathematics).
- Universal_coefficient_theorem wikiPageWikiLink Manifold.
- Universal_coefficient_theorem wikiPageWikiLink Orientability.
- Universal_coefficient_theorem wikiPageWikiLink Poincaré_duality.
- Universal_coefficient_theorem wikiPageWikiLink Prime_number.
- Universal_coefficient_theorem wikiPageWikiLink Real_projective_space.
- Universal_coefficient_theorem wikiPageWikiLink Simplicial_homology.
- Universal_coefficient_theorem wikiPageWikiLink Singular_homology.
- Universal_coefficient_theorem wikiPageWikiLink Splitting_lemma.
- Universal_coefficient_theorem wikiPageWikiLink Tensor_product_of_modules.
- Universal_coefficient_theorem wikiPageWikiLink Topological_space.
- Universal_coefficient_theorem wikiPageWikiLink Tor_functor.
- Universal_coefficient_theorem wikiPageWikiLink Torsion_(algebra).
- Universal_coefficient_theorem wikiPageWikiLinkText "Universal coefficient theorem".
- Universal_coefficient_theorem wikiPageWikiLinkText "Universal coefficient theorem#Universal coefficient theorem for cohomology".
- Universal_coefficient_theorem wikiPageWikiLinkText "universal coefficient theorem".
- Universal_coefficient_theorem wikiPageUsesTemplate Template:=.
- Universal_coefficient_theorem wikiPageUsesTemplate Template:Cite_journal.
- Universal_coefficient_theorem wikiPageUsesTemplate Template:Math.
- Universal_coefficient_theorem wikiPageUsesTemplate Template:Mvar.
- Universal_coefficient_theorem wikiPageUsesTemplate Template:Reflist.
- Universal_coefficient_theorem subject Category:Homological_algebra.
- Universal_coefficient_theorem subject Category:Theorems_in_algebraic_topology.
- Universal_coefficient_theorem type Theorem.
- Universal_coefficient_theorem comment "In algebraic topology, universal coefficient theorems establish relationships between homology and cohomology theories.".
- Universal_coefficient_theorem label "Universal coefficient theorem".
- Universal_coefficient_theorem sameAs Q2495664.
- Universal_coefficient_theorem sameAs Universelles_Koeffiziententheorem.
- Universal_coefficient_theorem sameAs 普遍係数定理.
- Universal_coefficient_theorem sameAs 보편_계수_정리.
- Universal_coefficient_theorem sameAs m.03xqk0.
- Universal_coefficient_theorem sameAs Теорема_об_универсальных_коэффициентах.
- Universal_coefficient_theorem sameAs Q2495664.
- Universal_coefficient_theorem wasDerivedFrom Universal_coefficient_theorem?oldid=688465772.
- Universal_coefficient_theorem isPrimaryTopicOf Universal_coefficient_theorem.