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Results tagged with homology
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user 9417
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.
5
votes
Accepted
When do submanifolds lie in the same homology class?
So the very simple answer is that $S$ and $S'$ are the same homology class if and only if they are the boundary of some sum of singular simplices. …
- 4,898
17
votes
1
answer
677
views
Ordinal-indexed homology theory?
Does there exist a good homology theory $H_{\alpha}(X)$ where $\alpha$ is an ordinal? …
- 4,898
12
votes
Homology of Covering Spaces
This is not a trivial problem. A favorite example of mine is the case of a knot complement, $S^3\setminus K$. (It is known that these are Eilenberg-Maclane spaces.) If you pick $A$ to be the commutato …
- 4,898