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Results tagged with homology
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user 21095
Homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
10
votes
1
answer
847
views
finite complex with non-finitely generated homology with local coefficients
I am looking for an explicit example, if one exists, of a (pointed) finite connected CW-complex $X$ such that some homology group with local coefficients $H_n(X,{\mathbb Z}[\pi_1 X])$ is not a finitely … Such an example would in particular give a finitely presented group $\pi$, and a chain complex of finitely generated free ${\mathbb Z}[\pi]$-modules whose homology groups are not all finitely generated …
- 6,210
13
votes
Accepted
Does the bordism homology theory satisfy the weak equivalence axiom?
This answer is simply to write the details for my comment above. It amounts to doing a little more work with homotopy equivalences, so as to carry out essentially the argument you gave in your comment …
- 6,210