Timeline for Torsion in cohomology of smooth manifolds
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 20, 2012 at 16:51 | comment | added | LMN | @Johannes, in regards to your answer to #1, you get that the map $f$ induces an isomorphism on the first $n-1$ homotopy groups. I don't see how this allows you to deduce that the cohomology groups of $M$ are the same as those of $K$. Hurewicz's theorem doesn't seem to help. | |
| Dec 19, 2012 at 23:26 | comment | added | Johannes Ebert | Odd-dimensional manifolds have two middle dimensions to control, so in that case, the situation is more complicated. | |
| Dec 19, 2012 at 21:35 | comment | added | LMN | Daniel, right - "odd" should be "even". | |
| Dec 19, 2012 at 21:31 | comment | added | Daniel Litt | @LMN: Even-dimensional manifolds are the ones with "middle cohomology groups." | |
| Dec 19, 2012 at 21:19 | comment | added | LMN | Johannes, I'm having a little trouble translating the language into things I am familiar with. Are you saying that the answer to my question #1 is yes (but if the dimension is odd we might not be able to control the middle cohomology group). | |
| Dec 19, 2012 at 21:07 | history | edited | Dmitri Pavlov | CC BY-SA 3.0 |
fixed a markup problem
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| Dec 19, 2012 at 21:01 | history | answered | Johannes Ebert | CC BY-SA 3.0 |