Timeline for Are there oriented $4k+2$ manifolds such that $im(H_{2k+1}(M; Z/2)\to H_{2k+1}(M, \partial M; Z/2))$ has odd dimension?
Current License: CC BY-SA 2.5
7 events
when toggle format | what | by | license | comment | |
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Jan 30, 2011 at 6:30 | vote | accept | Greg Friedman | ||
Jan 29, 2011 at 1:11 | answer | added | Tom Goodwillie | timeline score: 7 | |
Jan 28, 2011 at 0:57 | answer | added | Martin O | timeline score: 8 | |
Jan 27, 2011 at 5:01 | comment | added | Greg Friedman | Fair question. I'm interested in bordism groups of Z/2-Witt spaces. If a Z/2 Witt space is defined to only be Z/2 oriented, then I can compute those bordism groups, which are isomorphic to Z/2. But it's not clear that a Z/2 Witt space shouldn't be defined to be Z-oriented but satisfy the Z/2 Witt condition. Thus I would like to compute such a bordism group. I can show that it's 0 or Z/2. The possible invariant is the middle dimensional Z/2 intersection homology pairing in W(Z/2)=Z/2. This question would determine whether there is a Witt space with only point singularities representing 1. | |
Jan 27, 2011 at 4:02 | comment | added | Ben Wieland | Dylan, $RP^6$ (or $RP^2$) is a counterexample, with empty boundary, even. | |
Jan 27, 2011 at 2:52 | comment | added | Dylan Wilson | If you're working mod 2 why do you care that they are oriented? | |
Jan 26, 2011 at 23:04 | history | asked | Greg Friedman | CC BY-SA 2.5 |