Timeline for Construct a homeomorphism of a surface that sends a subsurface to another subsurface
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 15, 2022 at 17:18 | comment | added | Sam Nead | Those are some of the steps needed to produce an explicit homeomorphism. I suggest you look at the following paper: arxiv.org/abs/1604.04314 by Mark Bell. Note that many of the algorithms are implemented in the software packages described here: markcbell.github.io | |
| Mar 11, 2022 at 17:10 | vote | accept | CommunityBot | ||
| Mar 11, 2022 at 15:17 | comment | added | Sam Nead | Finally, if my answer answers your question, it would be polite to accept it (by checking the tick mark near the voting buttons). | |
| Mar 11, 2022 at 15:15 | comment | added | Sam Nead | Regarding Lee Mosher's paper - I was thinking of Lemma "combing terminates" on page 321 of his 1995 Annal's paper. You will need to read a bit more than just that to understand the context. | |
| Mar 11, 2022 at 15:12 | comment | added | Sam Nead | If you don't like this definition of mapping class, then you could call it something else. What matters is having the ability to permute boundary components (of $B$, say) according to the "instructions" given by the list of complexities. | |
| Mar 11, 2022 at 15:11 | comment | added | Sam Nead | @Osiris - The "correct" definition of mapping class in this case is "homeomorphisms up to isotopy". Thus a mapping class can permute boundary components. | |
| Mar 9, 2022 at 22:47 | comment | added | Sam Nead | This follows from the classification of surfaces, and from the fact that orientation-preserving mapping classes (correctly defined) can arbitrarily permute boundary components. | |
| Mar 9, 2022 at 18:35 | history | answered | Sam Nead | CC BY-SA 4.0 |