Timeline for Typical preimage of the commutator map
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 2, 2020 at 17:29 | comment | added | YCor | Do we have a good reason to expect that generic fibers are connected? | |
| Jun 2, 2020 at 16:18 | comment | added | Dmitri Scheglov | @MoisheKohan Thanks for the link. If indeed the factorized variety is homeomorphic to $S^2$ in this case then it would not be very surprizing if the preimage is actually homeomorphic to $S^3=SU(2)$ somehow Hopf-fibered over this $S^2$.. | |
| Jun 2, 2020 at 16:12 | comment | added | Moishe Kohan | Goldman wrote extensively on these; apparently, according to this paper, for $G=SU(2)$, the variety is homeomorphic to $S^2$, but no proof is given. | |
| Jun 2, 2020 at 16:04 | comment | added | Dmitri Scheglov | @MoisheKohan , indeed this is how the question appeared, as I need to understand something about character varieties of one-punctured torus, fixing the holonomy element along the loop around the puncture. Could you provide me some standard references, if there are any , of course.. | |
| Jun 2, 2020 at 16:00 | comment | added | Moishe Kohan | It is natural to divide this preimage by the $G$-action (via conjugation); then it becomes the "relative character variety" of the once-punctured torus. Topology of such varieties was/is extensively studied, but I do not remember the answer off-hand. | |
| Jun 2, 2020 at 15:43 | history | asked | Dmitri Scheglov | CC BY-SA 4.0 |