Timeline for Are there periodicity phenomena in manifold topology with odd period?
Current License: CC BY-SA 3.0
12 events
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| Dec 13, 2022 at 17:19 | comment | added | Connor Malin | Corollary 1.5 of Behrens-Mahowald-Quigley asserts there are ~50 families of exotic spheres that are 192 periodic, which I would say is certainly an $\textit{odd}$ period. | |
| Nov 12, 2014 at 18:03 | comment | added | John Palmieri | Are these periodicities reflected in, or reflections of, non-nilpotent elements in some graded commutative rings? If so, the period would have to be even. | |
| Nov 6, 2014 at 14:37 | comment | added | Ryan Budney | A 12 mod 16 comes up in a cobordism group. See the comments here: mathoverflow.net/questions/165609/… | |
| Nov 2, 2014 at 9:02 | comment | added | Qiaochu Yuan | @Urs: well, in the context of periodic ring spectra there's a straightforward reason to favor even periodicity: if any element $\beta$ of odd degree in a graded commutative ring is invertible with respect to multiplication, then $\beta^2$ being $2$-torsion implies the entire ring is $2$-torsion. I guess more geometrically this argument suggests the evenness is about the graded commutativity of the intersection pairing. | |
| Nov 2, 2014 at 8:42 | comment | added | Urs Schreiber | Regarding inducing periodicity on manifolds from universal orientations of periodic ring spectra: there is MO discussion here mathoverflow.net/a/46453/381 which (see the exchange in the comments) favors even periodicity. (This is not a proof of anything, I suppose, but maybe a hint.) | |
| Nov 1, 2014 at 23:22 | comment | added | Paul Siegel | There are lots of maps involving the surgery exact sequence which are isomorphisms away from the prime $2$ but which do strange things at $2$. A big part of this is of course that quadratic forms over group algebras behave strangely in characteristic $2$. I wonder if this is the underlying explanation for your observations about periodicity. | |
| Nov 1, 2014 at 22:54 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Nov 1, 2014 at 4:11 | comment | added | Qiaochu Yuan | Right, I guess I already don't know a concrete example there. | |
| Oct 31, 2014 at 15:43 | comment | added | André Henriques | A better question might be: what are some periodicity phenomena in manifold topology with period not a power of two? | |
| Oct 31, 2014 at 5:34 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Oct 31, 2014 at 5:24 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Oct 31, 2014 at 5:18 | history | asked | Qiaochu Yuan | CC BY-SA 3.0 |