Timeline for Exponentiation in finite simplicial sets
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 14, 2015 at 6:17 | vote | accept | Ilan Barnea | ||
| Jul 14, 2015 at 6:16 | comment | added | Ilan Barnea | Thanks! I think I understand the argument, I just don't see why you had to assume $x_n = [\partial \Delta_4]$. I also believe it should be $\sigma : [n+1] \rightarrow [4]$ (or perhaps I misunderstand something?). | |
| Mar 4, 2015 at 23:45 | comment | added | Eric Wofsey | I think you can also get exponential growth for $X=\Delta_3/\partial \Delta_3$ by a slightly different construction. Don't require $d_{i+1}x_i=d_{i+1}x_{i+1}$ to always be $[\partial \Delta_3]$, and instead consider the set $S$ of all values of $i$ such that it is $[\partial\Delta_3]$. It is not hard to see that $S$ can be almost any subset of $\{0,\dots,n\}$, so $Hom(\Delta_1\times \Delta_n, X)$ must have at least $\approx 2^n$ elements. | |
| Mar 4, 2015 at 23:24 | comment | added | Eric Wofsey | Very nice! I guess in the argument I had in mind on my comment on Charles's answer I was implicitly imagining $X$ was actually a simplicial complex. | |
| Mar 4, 2015 at 23:10 | review | Late answers | |||
| Mar 4, 2015 at 23:12 | |||||
| Mar 4, 2015 at 23:00 | review | First posts | |||
| Mar 4, 2015 at 23:08 | |||||
| Mar 4, 2015 at 22:54 | history | answered | user68822 | CC BY-SA 3.0 |