Timeline for Factoring maps of handlebodies
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 19, 2009 at 18:21 | vote | accept | HJRW | ||
| Nov 19, 2009 at 1:21 | answer | added | Sam Nead | timeline score: 4 | |
| Nov 19, 2009 at 0:47 | comment | added | HJRW | That's exactly the order I had in mind! | |
| Nov 19, 2009 at 0:46 | history | edited | HJRW | CC BY-SA 2.5 |
added 148 characters in body
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| Nov 19, 2009 at 0:31 | comment | added | Sam Nead | (Or does that mess up the desired order?) | |
| Nov 19, 2009 at 0:31 | comment | added | Sam Nead | Ok, will the following suffice: homotope first, compress second and then realize that the result includes in a finite-index cover? | |
| Nov 19, 2009 at 0:27 | comment | added | HJRW | Sam, I see what you mean - I'm a little confused about what the correct statement about the boundary should be. I realise now that my original comment didn't make sense. Well, as I said, I'd be happy for any factorization to start with, and to worry about the boundary later. | |
| Nov 19, 2009 at 0:02 | comment | added | Sam Nead | What about taking a regular neighborhood of the (p,q) curve on the boundary (p times about the meridian, q times about the longitude). So this is incompressible... I suppose that you will homotope this to be a q-fold covering. I don't see how you are going to do this keeping the boundary "nice". | |
| Nov 18, 2009 at 23:45 | comment | added | HJRW | I'd be happy to start with any factorization, and worry about whether the homotopy can be made nice later. | |
| Nov 18, 2009 at 23:30 | comment | added | Sam Nead | So the maps has to start by mapping the boundary to the boundary? For example, what about placing a trefoil knot in a three-ball, and thickening it a bit? A homotopy can unknot this (and then I guess you want to compress), but not in any boundary respecting way... | |
| Nov 18, 2009 at 20:27 | comment | added | HJRW | At each "time", the homotopy should map the boundary to itself. | |
| Nov 18, 2009 at 20:21 | comment | added | Sam Nead | What does "respect the boundary" mean? | |
| Nov 18, 2009 at 20:07 | history | asked | HJRW | CC BY-SA 2.5 |