Timeline for Homeomorphisms of $S^n\times S^1$
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 20, 2017 at 16:24 | comment | added | Ben Wieland | The obstruction to isotopy is not just $Wh_2(\pi_1)$, as indicated by the title of Allen Hatcher's first paper. He mentions $S^n\times S^1$ as the very simplest example of the obstruction being realized here. | |
| Feb 4, 2017 at 6:28 | comment | added | olga | Indeed I need the result that for $n>3$ there is no difference between smooth and TOP pseudoisotopies of homeomorphisms $S^n\times S^1$. | |
| Feb 1, 2017 at 10:30 | vote | accept | olga | ||
| Feb 5, 2017 at 18:48 | |||||
| Feb 1, 2017 at 10:30 | vote | accept | olga | ||
| Feb 1, 2017 at 10:30 | |||||
| Feb 1, 2017 at 4:20 | comment | added | Igor Belegradek | The difference between smooth and TOP pseudoisotopies is probably nontrivial. In any case all known computations are in the pseudoisotopy stable range, where the map on the homotopy groups induced by the inclusion from the smooth to TOP pseudoisotopies has finitely generated kernel and cokernel, see corollary 4.2 in arxiv.org/pdf/math/0607367v4 for a precise statement. | |
| Feb 1, 2017 at 3:23 | comment | added | Ben Wieland | Hatcher-Wagoner probably already proved that $Wh_2(\mathbb Z)=0$, but it is also covered by Loday. It is just the fact that the higher $K$-theory of $\mathbb Z[\mathbb Z]=\mathbb Z[t^\pm]$ is easily described in terms of $K(\mathbb Z)$. | |
| Feb 1, 2017 at 2:09 | history | answered | Danny Ruberman | CC BY-SA 3.0 |