Timeline for Fixed point of $S^1$-action using roots of unity
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 18, 2013 at 19:42 | vote | accept | Chris Gerig | ||
| Jan 18, 2013 at 10:14 | history | edited | Mark Grant | CC BY-SA 3.0 |
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| Jan 17, 2013 at 7:09 | comment | added | Mark Grant | The definition of limit being used is in subsection 2.2. It seems that $\lim U_p = S^1$ since every point of $S^1$ has a neighbourhood which intersects all but finitely many of the $U_p$. And the disk should certainly be a $n$-cohomology manifold with boundary, which just leaves the question of whether these results go over to the boundary case. Perhaps this is covered in the given references. | |
| Jan 17, 2013 at 5:21 | comment | added | Chris Gerig | Actually I'm not sure the Poincare duality between homology and compactly supported cohomology is true, since X has boundary. | |
| Jan 16, 2013 at 21:33 | comment | added | Chris Gerig | Ah yes, I have this neat book (as well as Bredon's one) which is where I picked up Smith theory 4 years ago. Two quick questions: Do we actually have a rigorously defined $\lim U_p =S^1$ ? (I'm not sure what the definition of limit is being used here). If that fits with the limit-hypothesis of the stated theorem, then this theorem is actually the desired proof for both of my questions, right? (I believe our $X$ is an n-cohomology manifold over $\mathbb{Z}$ since $H^{n-k}_c(X)=H_k(X)$, and we can choose the compact subset $C$ to be $X$ itself). | |
| Jan 16, 2013 at 11:50 | history | answered | Mark Grant | CC BY-SA 3.0 |