Timeline for Decomposition of simplicial G-set?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 14, 2011 at 1:29 | vote | accept | Gao 2Man | ||
| Dec 11, 2011 at 4:49 | answer | added | S. Carnahan♦ | timeline score: 0 | |
| Dec 11, 2011 at 4:18 | comment | added | S. Carnahan♦ | You definition of simplicial $G$-set is missing the condition that the face and degeneracy maps in $X$ are compatible with the maps in $G$. | |
| Dec 10, 2011 at 12:34 | comment | added | Tom Goodwillie | You may consider the set $G_n/X_n$ of orbits, and these constitute a simplicial set $G/X$. If, as Justin asks, you mean finitely many orbits, then the answer is yes: any simplicial set is a union of simplicial subsets that are both finite and of finite type in your terminology; in particular this is true for the simplicial set $G/X$. (By the way, your "finite simplicial set" means that $|X|$ is a finite-dimensional cell complex, your "finite type simplicial set" means finitely many cells in each dimension, and the two together mean that $|X|$ is a finite cell complex, i.e. a compact space.) | |
| Dec 10, 2011 at 8:48 | comment | added | André Henriques | The condition "elements of high levels are all degenerate" also seems a bit too strong. If $G$ has non-degenerate simplices in all degrees, then so will any non-trivial simplicial $G$-set... | |
| Dec 10, 2011 at 8:26 | comment | added | Justin Noel | Do you mean $X_n$ has finitely many orbits? Otherwise any infinite group (considered as a constant simplicial group) acting on itself would be a counterexample. | |
| Dec 10, 2011 at 5:28 | history | asked | Gao 2Man | CC BY-SA 3.0 |