Timeline for Salvetti complex of dihedral Artin group
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4 at 13:37 | comment | added | Thomas Haettel | You are right, the Euler characteristic is $0$. On each edge there are locally $n$ copies of the $2n$-gon glued. So if $n \geq 3$, it is not a surface. | |
| Dec 4 at 8:17 | comment | added | Marcos | Maybe there is some mistake on my reasoning. But you are adding a $2n$-gon with some identifications. Hence, since this $2n$-gon has $1$ face, $2$ edges and $1$ vertex the Euler characterisitic of this cell is $0$. Thus, the cell we are identifying must be homeomorphic either to a torus or to a Klein bottle, since they are the only surfaces with Euler characteristic equal to $0$. Right? | |
| Dec 1 at 21:49 | history | answered | Thomas Haettel | CC BY-SA 4.0 |