Timeline for Adding morphisms to a category without changing homotopy type
Current License: CC BY-SA 3.0
14 events
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| Jul 20, 2013 at 18:29 | comment | added | Dan Ramras | Vidit, could you maybe say a bit about where the question comes from (especially the second question)? | |
| Jul 19, 2013 at 23:51 | comment | added | Dan Ramras | I think the Quillen fiber over 0, in Benjamin Steinberg's example, has two objects and one morphism going between them, so it's contractible. The same is true for the Quillen fiber over 1. So it seems like Theorem A tells us that in the simplest example, the procedure in question doesn't change the homotopy type (hope I got this right...). | |
| Jul 19, 2013 at 23:32 | history | edited | Vidit Nanda |
added simplicial tag
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| Jul 19, 2013 at 23:31 | comment | added | Vidit Nanda | @ToddTrimble No worries, thank you for thinking about the question. Since I'm still stumped, I think I'll do what I do best: wait and hope that Tom Goodwillie sees this question :) | |
| Jul 19, 2013 at 23:11 | comment | added | Todd Trimble | @Vidit thanks; removing earlier comment. | |
| Jul 19, 2013 at 23:06 | comment | added | Vidit Nanda | @ToddTrimble I am also confused, but it seems that $fg$ lies entirely in the boundary of $fgf$, which deforms to $f$. | |
| Jul 19, 2013 at 22:45 | comment | added | Dan Ramras | I've convinced myself that Benjamin Steinberg's example has trivial fundamental group, at least... | |
| Jul 19, 2013 at 20:05 | comment | added | Benjamin Steinberg | Maybe it is. I must think more. | |
| Jul 19, 2013 at 19:59 | comment | added | Vidit Nanda | @BenjaminSteinberg why isn't it contractible? | |
| Jul 19, 2013 at 19:14 | comment | added | Benjamin Steinberg | But if you start with the two-element poset $0<1$, which has a contractible classifying space, and do your construction with respect to the unique non-identity arrow, then don't you get something which is no longer contractible? | |
| Jul 19, 2013 at 19:13 | history | edited | Vidit Nanda | CC BY-SA 3.0 |
non-degeneracy condition on loops
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| Jul 19, 2013 at 19:12 | comment | added | Vidit Nanda | Okay, yes, I forgot to add that all x_j and y_j are distinct | |
| Jul 19, 2013 at 19:11 | comment | added | Benjamin Steinberg | I don't quite get this. If $f:x\to y$ is a morphism, then you have a zig-zag $x\rightarrow y\leftarrow x$ | |
| Jul 19, 2013 at 18:55 | history | asked | Vidit Nanda | CC BY-SA 3.0 |