Timeline for Homology spheres and fundamental group
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 9, 2015 at 21:12 | vote | accept | Dario | ||
| Jul 9, 2015 at 17:34 | answer | added | Danny Ruberman | timeline score: 20 | |
| Jul 9, 2015 at 16:20 | comment | added | mme | Pick an irreducible representative of an element $[M]$ of the homology cobordism group $\Theta_{\Bbb Z}^3$ that is not 2-torsion. Then it does not support an orientation-reversing homeomorphism. Examples are the Brieskorn spheres $\Sigma(p,q,pqk-1)$ for $k \geq 1$ and $p,q$ relatively prime. Then $M \# M$ and $M \# \overline{M}$ provide counterexamples by prime decomposition. (If you demanded irreducible then your answer is of course 'yes' for 3-manifolds because other than $\Sigma(2,3,5)$ and $S^3$, these are aspherical and the Borel conjecture is known in 3 dimensions). | |
| Jul 9, 2015 at 15:37 | history | asked | Dario | CC BY-SA 3.0 |