Timeline for Connection between complex orientations and R-orientations for a ring spectrum R?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 14, 2013 at 18:00 | vote | accept | Jonathan Beardsley | ||
| Feb 13, 2013 at 8:13 | history | edited | Ricardo Andrade |
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| Feb 13, 2013 at 5:35 | answer | added | Peter May | timeline score: 8 | |
| Feb 13, 2013 at 5:14 | comment | added | Peter May | This doesn't help answer your real question but gives your map f. F= GL_1S is the subspace of QS^0 = colim \Omega^n\Sigma^n consisting of stable maps of spheres of degree 1 or -1. Let SF(n) be the monoid under composition of maps S^n\to S^n of degree 1. Using one-point compactification of C^n$, U(n) embeds in SF(2n); passing to colimits gives U \to SF; passing to classifying spaces gives f: BU \to BSF. But the map is irrelevant to the classical construction of the Thom spectrum MU, which just uses the Thom spaces of the universal complex n-plane bundles directly. | |
| Feb 12, 2013 at 20:51 | comment | added | Jonathan Beardsley | And yeah, thanks Mark. I'm trying to figure out how that's related. | |
| Feb 12, 2013 at 20:49 | comment | added | Jonathan Beardsley | Sorry, ABGHR is the paper: arxiv.org/abs/0810.4535 | |
| Feb 12, 2013 at 19:57 | comment | added | Mark Grant | What is ABGHR? I guess you already know that a complex orientation on $E$ is the same as a map of ring spectra $MU\to E$. | |
| Feb 12, 2013 at 19:21 | history | asked | Jonathan Beardsley | CC BY-SA 3.0 |