Timeline for Equivariant obstruction theory done wrong
Current License: CC BY-SA 3.0
4 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Mar 6, 2017 at 9:34 | comment | added | Mark Grant | @Tyler: That could well be. I was also wondering if difference cochains show up. For example, let $G=C_2$ generated by $\sigma$, then any (partial)section $s:B\to E$ can be "conjugated by $\sigma$" to produce another section $s^\sigma:B\to E$, and $s$ is equivariant iff $s=s^\sigma$. Now the difference cochain $\delta(s,s^\sigma)\in H^k(B,\pi_k(F))$ is defined, and probably is in $\ker(1+\sigma)$ so represents an element of $H^1(G;H^k(B,\pi_k(F))$. This is the kind of thing I was wondering about. It's all a bit reminiscent of the construction of Steenrod powers. | |
| Mar 2, 2017 at 19:38 | comment | added | Tyler Lawson | Is it possible that it comes from the restriction map from the Bredon cohomology of $B$ to the Bredon cohomology of $EG \times B$, which can be identified (up to appropriate twisting) with the cohomology of the Borel construction? | |
| Mar 2, 2017 at 15:05 | history | asked | Mark Grant | CC BY-SA 3.0 |