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Results tagged with homology
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user 1708
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.
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Examples of the varying strengths of topological invariants
Using the Gysin sequence, one finds that the cohomology groups (and homology groups) are the same as those of $S^2\times S^4$, mainly, a $\mathbb{Z}$ in dimension 0,2,4, and 6, and 0 elsewhere. … And just to anticipate, the spaces $S^3\times \mathbb{R}P^2$ and $S^2\times \mathbb{R}P^3$ have all the same homotopy groups, but are not homotopy equivalent (as homology will tell you). …