Timeline for geometric conditions on maps between manifolds inducing monomorphisms on cohomology
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 29, 2015 at 6:53 | vote | accept | QSR | ||
| Oct 28, 2015 at 13:59 | comment | added | Danny Ruberman | You could say a bit more by this argument. Say $N$ has dimension $n$. The same cup-product calculation says that if $f^*$ is injective on $H^n(N,Z/p)$, it is injective in all degrees. The non-vanishing of $f^*$ on $H^n(N,Z/p)$ could be phrased as the existence of an n-dimensional submanifold of $M$ mapping with non-zero Z/p degree onto $N$. This follows from the existence of a section, or more generally of a `multi-section' of degree relatively prime to $p$. | |
| Oct 28, 2015 at 10:39 | history | edited | Myshkin | CC BY-SA 3.0 |
minor latex edit
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| Oct 28, 2015 at 8:58 | history | edited | Thomas Rot | CC BY-SA 3.0 |
small additions
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| Oct 27, 2015 at 22:44 | history | answered | Thomas Rot | CC BY-SA 3.0 |