Timeline for Homologically trivial submanifolds
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 11, 2010 at 21:50 | comment | added | Ian Agol | @ Jeffrey: If N is not separating, then its homology class is non-trivial, since one can find a closed loop intersecting it once. So I'm implicitly using that $[N]=0$. | |
| Jun 11, 2010 at 9:51 | comment | added | Jeffrey Giansiracusa | A codimension 1 submanifold need not separate the ambient manifold into 2 pieces - e.g., think of $N \times \{1\}$ inside $N \times S^1$. | |
| Jun 11, 2010 at 7:50 | comment | added | Ryan Budney | Er, well, it was before Thom's big paper. :) A long time ago. | |
| Jun 11, 2010 at 6:11 | comment | added | Robin Chapman | Ryan, J.-P. Serre (b. 1926) must have been an even more prodigious talent than I had realized :-) | |
| Jun 11, 2010 at 1:59 | comment | added | Ryan Budney | That homology classes in $H_k(X)$ or $H_k(X,\partial X)$ with integer coefficients are realizable when $k \leq 5$ I believe this is due to Cartan and Serre, back in the early 30's. Similarly for co-dimension 1 classes. I believe Serre also proved that provided $k$ is less than half the dimension of $X$, some (explicit) non-zero multiple of it is realizable by a submanifold with a trivial normal bundle. | |
| Jun 11, 2010 at 1:30 | history | answered | Ian Agol | CC BY-SA 2.5 |