Let , be topological spaces. One can ask a question: how homology of are related to homologies of and . The answer to this question depends on the homology theory we’re talking about and also the coefficients ring. On the other hand, it is well known, that all homology theories are isomorphic on CW-complexes. Thus we may restrict to CW-complexes. Nevertheless the following theorem is more general:
Theorem. (Kunneth) Assume, that , are topological spaces and is a principal ideal domain. Denote by the singular homology with coefficients in . Then, for any there exists following short exact sequence in the category of -modules:
for any .
|Date of creation||2013-03-22 19:13:57|
|Last modified on||2013-03-22 19:13:57|
|Last modified by||joking (16130)|