Timeline for Cellularity of anodyne extensions?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 24, 2018 at 16:08 | comment | added | Tyler Lawson | @HarryGindi yes, that's correct, I meant the geometric realization of an iterated pushout along horn inclusions. Sorry for the confusion. | |
| Oct 24, 2018 at 15:38 | vote | accept | Harry Gindi | ||
| Oct 24, 2018 at 15:17 | answer | added | Simon Henry | timeline score: 6 | |
| Oct 24, 2018 at 12:54 | comment | added | Harry Gindi | @PhilippeGaucher It doesn't appear on the mobile version of the website. | |
| Oct 24, 2018 at 12:49 | comment | added | Philippe Gaucher | @HarryGindi you wrongly use the feature "@", by not letting the viewer complete the name. Tyler won't be aware of your post in the top part of the window unless he rereads your question. | |
| Oct 24, 2018 at 11:01 | comment | added | Harry Gindi | @Tyler Did you mean that the geometric realization of a pushout of a horn inclusion is always simple, rather than all anodynes? Otherwise, this would not produce a counterexample. | |
| Oct 24, 2018 at 10:56 | comment | added | Tyler Lawson | When you take the geometric realization of an anodyne extension of simplicial sets, you get what is called a simple homotopy equivalence (more or less by definition). There is an invariant of homotopy equivalences called Whitehead torsion which must vanish for a map $f$ to be homotopic to a simple homotopy equivalence. I'm guessing that you can get a counterexample by taking a homotopy equivalence with nontrivial Whitehead torsion, finding a simplicial model for it, and taking the mapping cylinder to get an inclusion whose realization is a homotopy equivalence not homotopic to a simple one. | |
| Oct 24, 2018 at 10:25 | history | asked | Harry Gindi | CC BY-SA 4.0 |