Timeline for If the universal cover has three boundary components, does it have infinitely many?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 12, 2023 at 19:04 | vote | accept | Sam Nead | ||
| Oct 12, 2023 at 18:54 | comment | added | Andy Putman | @SamNead: Yes, I think that's a good way to do it! | |
| Oct 12, 2023 at 18:51 | comment | added | Sam Nead | My (too long) proof worked directly with $M$. I used the canonical compression body (following Bonahon) and, if that was trivial, the canonical $I$-bundle as in JSJ theory. Your proof (plus Moishe's remark) is shorter. I think the following is good. Lift to get some boundary component $B$ to surject the fundamental group. The cover is thus a compression body. If it is a handlebody or a product, we have a contradiction. So it has an interior boundary component, $C$. The fundamental group of $C$ has infinite index, so we win. | |
| Oct 12, 2023 at 18:44 | history | edited | Andy Putman | CC BY-SA 4.0 |
added 30 characters in body
|
| Oct 12, 2023 at 18:09 | history | answered | Andy Putman | CC BY-SA 4.0 |