Timeline for Can a homotopy inverse of the map from a Lie group to loops on its classifying space be given by holonomy?
Current License: CC BY-SA 2.5
7 events
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| Jan 24, 2011 at 15:04 | comment | added | Todd Trimble | Jim, the question was not whether $\Omega BG$ is ($A_\infty$) homotopy equivalent to $G$ -- that much I indicated I already knew. It's a question of giving an explicit pair of maps which exhibits the equivalence. When I took algebraic topology as a graduate student, much of this type of thing was left in a black box: one can easily describe an appropriate map $i: G \to \Omega BG$, and give an abstract argument for why this is a homotopy equivalence, but as I've gotten older I like to get more concrete, giving a homotopy inverse explicitly. Thanks for the reference! I'll have a look. | |
| Jan 24, 2011 at 1:44 | comment | added | Jim Stasheff |
$\Omega BG$ being $A_\infty$ homotopy equivalent to G for G(F) is indeed ancient' - see my birth certificate! though it's more subtle than for smooth bundles with connection see my now updated version of parallel transport revisited' at the n-lab so what is it you'ld like to do with it
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| Jan 20, 2011 at 22:07 | vote | accept | Todd Trimble | ||
| Jan 20, 2011 at 18:23 | answer | added | Bill Thurston | timeline score: 12 | |
| Jan 20, 2011 at 18:22 | answer | added | Johannes Ebert | timeline score: 2 | |
| Jan 20, 2011 at 18:18 | answer | added | John Klein | timeline score: 5 | |
| Jan 20, 2011 at 17:21 | history | asked | Todd Trimble | CC BY-SA 2.5 |