Timeline for simplicial spaces without degeneracies
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 1, 2015 at 7:28 | comment | added | archipelago | Maybe it is worth to remark for future readers that the case of homotopy equivalences instead of weak ones is true without any point-set topological restrictions since $X_k\times\partial\Delta^k\rightarrow X_k\times\Delta^k$ is always a Hurewicz cofibration. | |
| Mar 24, 2015 at 1:29 | comment | added | David Carchedi | Actually, it turns out that there are more problems, e.g. $X_k \times \partial \Delta^k \to X_k \times \Delta^k$ is not a Serre cofibration in general, and the above mentioned T1 property. However, you can get around both of these by using facts in Appendix A of citeseerx.ist.psu.edu/viewdoc/…. I need this fact in a paper I am writing, so the complete write up should appear on the arXiv soon. | |
| Mar 19, 2015 at 11:46 | comment | added | Oscar Randal-Williams | Yes, I daresay that's necessary. | |
| Mar 19, 2015 at 10:13 | comment | added | David Carchedi | Suppose that we are talking about fat geometric realization. For the second question, to deduce to checking that you get a weak homotopy equivalence on $k$-skeleta, you have to argue that any map from a sphere factors through a finite stage of the filtration, but I'm not sure how to argue this without assuming that points are closed, so I think you might need some T1 assumption somewhere? | |
| Mar 9, 2015 at 9:21 | vote | accept | Ulrich Pennig | ||
| Mar 19, 2012 at 21:01 | history | answered | Oscar Randal-Williams | CC BY-SA 3.0 |