Timeline for Relative, local coefficient Poincaré duality
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 8 at 8:01 | vote | accept | Qwert Otto | ||
| Aug 8 at 6:54 | comment | added | Dan Petersen | Preferred references for me could be Sheaves in topology (Dimca) or Cohomology of sheaves (Iversen), but you might not be a fan of the sheafy/derived category perspective. | |
| Aug 8 at 6:53 | comment | added | Dan Petersen | I prefer to think about this in terms of Borel-Moore homology/compact support cohomology. If $X$ is compact then $H_i(X,\partial X;S)$ is isomorphic to $H_i^{BM}(X^\circ,S)$ (where $X^\circ = X \setminus \partial X$). A nice version of Poincaré duality for noncompact manifolds is a cap-product isomorphism between cohomology and Borel-Moore homology, which in this case would say $H_i^{BM}(X^\circ,S) \cong H^{n-i}(X^\circ,S)$. But the latter coincides with $H^{n-i}(X,S)$ by homotopy invariance. | |
| Aug 7 at 14:29 | comment | added | Qwert Otto | Thank you for the answer; do you have any preferred reference for this? | |
| Aug 7 at 13:08 | history | answered | Dan Petersen | CC BY-SA 4.0 |