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 | |
|---|---|---|---|---|---|
| Oct 29, 2015 at 6:53 | vote | accept | QSR | ||
| Oct 28, 2015 at 5:44 | comment | added | Giovanni Moreno | @JasonStarr I agree with you: one way to have $f^*$ injective, is to require it to admit a left inverse, which is the same as requiring $f$ to admit, up to homotopy, a right inverse, i.e., a section. To see it more geometrically, one may work with the graph $\Gamma_f$ of $f$ inside the cylinder $M\times N$: then if there exists a deformation of the cylinder which makes $\Gamma_f$ projecting onto the second factor, your $f^*$ is injective. | |
| Oct 27, 2015 at 22:44 | answer | added | Thomas Rot | timeline score: 4 | |
| Oct 24, 2015 at 14:46 | comment | added | Jason Starr | If there is a section of $f$, then those homomorphisms are split monomorphisms. This is also true if there is a section after replacing $M$ and $N$ be homotopic topological spaces. | |
| Oct 24, 2015 at 8:37 | history | asked | QSR | CC BY-SA 3.0 |