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Results tagged with at.algebraic-topology
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user 177900
Homotopy theory, homological algebra, algebraic treatments of manifolds.
1
vote
1
answer
107
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When given degrees generate the cohomology ring of a manifold?
Let $M$ be a connected closed manifold of dimension $n$.
Suppose we have a subset $I\subset I_n=\{1, \dots, n\}$ such that for any two continuous maps $f, g:M\to M$ if $f^*=g^*|_{\oplus_{i\in I}H^i(M, …
- 21
-1
votes
1
answer
137
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Manifold for which you need to specify the action on cohomology in each degree
Let $M$ be a connected closed manifold of dimension $n\geq 2$.
Can it happen that for any $I\subsetneq I_n=\{1, \dots, n\}$ there are continuous maps $f, g:M\to M$ such that $f^*=g^*|_{\oplus_{i\in I} …
- 21
0
votes
0
answers
170
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Cohomology ring of 5-manifold generated in degrees 1, 2, 3
Is there a connected closed 5-manifold $M$ such that $\oplus_{i\geq 0} H^i(M, \mathbb{Z})$ is generated by $H^1(M, \mathbb{Z})\oplus H^2(M, \mathbb{Z})\oplus H^3(M, \mathbb{Z})$ but is not generated b …
- 21