Timeline for Factoring maps of handlebodies
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 19, 2009 at 18:21 | vote | accept | HJRW | ||
| Nov 19, 2009 at 18:21 | comment | added | HJRW | Excellent! I think this is the best possible statement I could have hoped for. | |
| Nov 19, 2009 at 17:54 | comment | added | Sam Nead | This is right. After producing f' we can 1) isotope each components of $f'(W') \cap D_i$ to be homeomorphic to its containing disk, 2) apply isotopy extension to the map $f'$, and 3) fix the boundaries of the components $f'(W') \cap P$. | |
| Nov 19, 2009 at 17:48 | history | edited | Sam Nead | CC BY-SA 2.5 |
Rewriting end to use Stallings paper.
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| Nov 19, 2009 at 16:31 | comment | added | HJRW | (I mean that the complement of X in P should be a ball after X has been compressed.) | |
| Nov 19, 2009 at 16:27 | comment | added | HJRW | Looks good! I want to use a homotopy to make X as big as possible in P, so the complement is either empty or a ball whose boundary contains one distinguished disc. If we do so then I think we get that, after a homotopy, the map factors as: glue on some 2-handles; glue on some 1-handles; and then a finite-sheeted covering. (Note that, in the question, I mentioned that by "inclusion", I meant gluing on 1-handles.) Does that sound right? | |
| Nov 19, 2009 at 1:30 | history | edited | Sam Nead | CC BY-SA 2.5 |
fix typo
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| Nov 19, 2009 at 1:21 | history | answered | Sam Nead | CC BY-SA 2.5 |