Timeline for Torsion in Atiyah Singer index formula
Current License: CC BY-SA 4.0
7 events
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| Apr 16, 2019 at 17:43 | history | edited | InfiniteLooper | CC BY-SA 4.0 |
typo
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| Oct 17, 2018 at 12:02 | comment | added | Oliver Nash | @vap You inspired me to ask about this here: mathoverflow.net/questions/313049/… Perhaps someone will illuminate us! | |
| Oct 17, 2018 at 9:06 | comment | added | Oliver Nash | @vap I'm afraid not! Years ago I learned (in an old paper of Karoubi [1]) that the fact that these two lattices coincide for spheres had strong topological consequences (obstruction to existence of almost complex structures) and I was struck by the result. I've occasionally wondered how far these ideas could go in general or how much they've been studied but I don't know. [1] archive.numdam.org/ARCHIVE/SHC/SHC_1963-1964__16_2/… | |
| Oct 16, 2018 at 21:17 | comment | added | vap | @OliverNash do you know a book or paper where these matters are discussed? (Meaning the relationship between the image of the Chern character and the integral cohomology) | |
| Oct 15, 2018 at 9:58 | history | edited | InfiniteLooper | CC BY-SA 4.0 |
added 8 characters in body
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| Oct 15, 2018 at 8:05 | comment | added | Oliver Nash | The fact that the Chern character maps $K$-theory to integral cohomology for spheres is stronger than just the lack of torsion. In general even if $X$ has no torsion, we have two maximal-rank lattices in $H^*(X, \mathbb{Q})$, namely $ch(K(X))$ and $H^*(X, \mathbb{Z})$. I expect any relationship between them should reflect interesting topology in $X$ (with the spheres being an extreme case). | |
| Oct 15, 2018 at 7:00 | history | asked | InfiniteLooper | CC BY-SA 4.0 |