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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 wikiPageID "996107".
- Universal_coefficient_theorem wikiPageRevisionID "603708247".
- Universal_coefficient_theorem hasPhotoCollection Universal_coefficient_theorem.
- Universal_coefficient_theorem subject Category:Homological_algebra.
- Universal_coefficient_theorem subject Category:Theorems_in_algebraic_topology.
- Universal_coefficient_theorem type Abstraction100002137.
- Universal_coefficient_theorem type Communication100033020.
- Universal_coefficient_theorem type Message106598915.
- Universal_coefficient_theorem type Proposition106750804.
- Universal_coefficient_theorem type Statement106722453.
- Universal_coefficient_theorem type Theorem106752293.
- Universal_coefficient_theorem type TheoremsInAlgebraicTopology.
- 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 label "Universelles Koeffiziententheorem".
- Universal_coefficient_theorem label "Теорема об универсальных коэффициентах".
- Universal_coefficient_theorem sameAs Universelles_Koeffiziententheorem.
- Universal_coefficient_theorem sameAs m.03xqk0.
- Universal_coefficient_theorem sameAs Q2495664.
- Universal_coefficient_theorem sameAs Q2495664.
- Universal_coefficient_theorem sameAs Universal_coefficient_theorem.
- Universal_coefficient_theorem wasDerivedFrom Universal_coefficient_theorem?oldid=603708247.
- Universal_coefficient_theorem isPrimaryTopicOf Universal_coefficient_theorem.