Universal coefficient theorem
GPTKB entity
Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
homology
cohomology |
| gptkbp:field |
gptkb:topology
|
| gptkbp:form |
long exact sequence
short exact sequence |
| https://www.w3.org/2000/01/rdf-schema#label |
Universal coefficient theorem
|
| gptkbp:involves |
gptkb:Ext_functor
gptkb:Tor_functor tensor product |
| gptkbp:notableFor |
relating homology and cohomology with different coefficients
|
| gptkbp:publishedIn |
gptkb:Annals_of_Mathematics
|
| gptkbp:relatedTo |
gptkb:Künneth_theorem
exact sequence cohomology with coefficients homology with coefficients |
| gptkbp:state |
homology with coefficients is determined by homology with integer coefficients and the coefficient group
cohomology with coefficients is determined by cohomology with integer coefficients and the coefficient group |
| gptkbp:usedIn |
singular cohomology
simplicial cohomology simplicial homology singular homology |
| gptkbp:bfsParent |
gptkb:K-theory_of_operator_algebras
|
| gptkbp:bfsLayer |
6
|