Timeline for Non-oriented version of Poincaré duality
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 10, 2011 at 23:14 | answer | added | Peter May | timeline score: 10 | |
| Apr 10, 2011 at 20:07 | comment | added | Faisal | For smooth manifolds the twisted version is also treated at the end of the first chapter of Bott & Tu. | |
| Apr 10, 2011 at 12:32 | answer | added | Neil Strickland | timeline score: 9 | |
| Apr 10, 2011 at 11:05 | answer | added | Johannes Ebert | timeline score: 7 | |
| Apr 10, 2011 at 10:34 | comment | added | Mark Grant | Also, any closed manifold satisfies Poincaré duality when homology and cohomology are taken with coefficients in the integers mod $2$. See Hatcher (math.cornell.edu/~hatcher/AT/ATpage.html) Chapter 3.3 (the twisted version is also treated in the additional topics for Chapter 3). | |
| Apr 10, 2011 at 8:59 | comment | added | Torsten Ekedahl | Yes, it gives an isomorphism between ordinary homology and cohomology of the local system of orientations (locally isomorphic to $\mathbb Z$) of closed manifolds. This local system is trivial precisely when the manifold is orientable. | |
| Apr 10, 2011 at 8:44 | history | asked | Randomblue | CC BY-SA 3.0 |