Timeline for Intersection pairing on $H_1$ of surfaces
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2022 at 3:09 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question has been bumped anyway)
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| Jun 8, 2022 at 14:32 | answer | added | Ethan Dlugie | timeline score: 1 | |
| Jun 8, 2022 at 14:25 | comment | added | Ethan Dlugie | Ah thanks, I think I see now that the map is probably an embedding and that, via the universal coefficient isomorphism $\operatorname{Hom}(H_1(X),R) \cong H^1(X;R)$, the image is compactly supported cohomology. It's Poincare duality for noncompact manifolds. | |
| Jun 8, 2022 at 1:27 | comment | added | Ryan Budney | Generally such a map won't be an isomorphism as the domain can be infinite-dimensional, so the two modules have ranks of different cardinalities. This map (the intersection pairing map) has finite support though, so you could restrict to that subspace of $Hom(H_1, R)$. | |
| Jun 8, 2022 at 0:47 | history | asked | Ethan Dlugie | CC BY-SA 4.0 |