Timeline for How many cells are needed in a simplicial structure of $\mathbb{S}^n$ to induce all of $\pi_n(\mathbb{S}^m)$
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| Sep 5, 2018 at 12:14 | comment | added | Henry Adams | I am interested in a related question also when n=m. In this case the homotopy group is the integers (which is infinite), and so we cannot expect a single cell decomposition on the domain to work for all maps f, which are determined (up to homotopy) by their degree. Nevertheless, we can fix a degree d, and ask what is a "minimal" simplicial decomposition of the domain admitting a map of degree d. | |
| Aug 15, 2018 at 22:58 | comment | added | j.c. | This question is also related (but not quite the same): mathoverflow.net/questions/285632/… | |
| Aug 15, 2018 at 22:10 | comment | added | Ryan Budney | Your question sits in a family of similar questions. I recall someone (?perhaps Mike Freedman?) asked a similar question but where he used some kind of elasticity measure of the smooth map, rather than simplicial structures. i.e. you're trying to make some kind of measurement of how complicated the map is, at some level. I can't find that old MO thread. | |
| Aug 15, 2018 at 21:45 | review | First posts | |||
| Aug 15, 2018 at 22:03 | |||||
| Aug 15, 2018 at 21:42 | history | asked | Takirion | CC BY-SA 4.0 |