Timeline for When does $BG \to BA$ loop to a homomorphism?
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Jul 22, 2019 at 12:07 | vote | accept | David Roberts♦ | ||
| Jul 5, 2019 at 19:38 | comment | added | Charles Rezk | I'll point to mathoverflow.net/questions/156408/…, which addresses a related question: what criteria imply that $\mathrm{Hom}(G,H)\to \mathrm{Map}_*(BG,BH)$ is a weak homotpy equivalence? The answer there says nothing about your case I think, but perhaps the methods used could be helpful. I don't know. | |
| Jun 21, 2019 at 8:07 | comment | added | David Roberts♦ | @Tyler hmm, interesting. It may be my hopes are misplaced, then. | |
| Jun 21, 2019 at 8:00 | comment | added | Tyler Lawson | Unfortunately I think that this question is quite sensitive to $A$ and not just to $BA$. For example, $A$ does not have any homomorphisms from $G$ if it does not have any homomorphisms from $S^1$, which requires that it have elements of finite order $(g^n = 1)$; however, any classifying space $BA$ is equivalent to a classifying space $BA'$ where $A'$ has no finite-order elements. | |
| Jun 21, 2019 at 7:49 | answer | added | Mark Grant | timeline score: 13 | |
| Jun 21, 2019 at 7:16 | comment | added | Praphulla Koushik | Oh. Ok ok :) @DavidRoberts | |
| Jun 21, 2019 at 7:14 | comment | added | David Roberts♦ | @PraphullaKoushik no, nothing at all. That answer is easy in comparison: they all do. | |
| Jun 21, 2019 at 7:14 | comment | added | David Roberts♦ | @Denis ok. And no, $G$ is not abelian. | |
| Jun 21, 2019 at 7:13 | comment | added | Praphulla Koushik | Does this have anything to do with similar question "when does a morphism of stacks $BG\rightarrow BH$ is coming from a morphism of Lie groups $G\rightarrow H$"??? | |
| Jun 21, 2019 at 7:13 | comment | added | Denis Nardin | $E_1$ or $A_∞$ (they are the same thing) control associativity. $E_∞$ is the commutative one. The other $E_n$ interpolate between the two (e.g. $E_2$ gives braided multiplication). $H_∞$ is the "shadow" of $E_∞$ in the homotopy category | |
| Jun 21, 2019 at 7:04 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
edited title
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| Jun 21, 2019 at 7:04 | comment | added | David Roberts♦ | @MarkGrant yes, sorry, my mistake. Edited the title, too. | |
| Jun 21, 2019 at 6:54 | history | edited | Denis Nardin | CC BY-SA 4.0 |
deleted 2 characters in body
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| Jun 21, 2019 at 6:50 | comment | added | David Roberts♦ | @DenisNardin yes, that's another way I was thinking of it. | |
| Jun 21, 2019 at 6:42 | comment | added | Denis Nardin | A more usual way of posing the question is: when does an $E_1$-homomorphism come from a map of topological groups? I don't know the answer though, but it is not always | |
| Jun 21, 2019 at 6:37 | comment | added | Mark Grant | Should that be "when is $BG\to BA$ the delooping of a homomorphism"? | |
| Jun 21, 2019 at 6:06 | history | asked | David Roberts♦ | CC BY-SA 4.0 |