Timeline for Guts of 3-manifolds for sutured manifolds and pared manifolds
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 21 at 14:49 | comment | added | Fredy | Of course! Thanks a lot! | |
| Feb 21 at 14:49 | vote | accept | Fredy | ||
| Feb 21 at 12:38 | comment | added | Sam Nead | Excellent - I think we are on the same page. If my answer has answered your question you should consider accepting it (by clicking the "check mark"). | |
| Feb 21 at 12:23 | comment | added | Fredy | Your answer certainly resolves my problem! But in Agol and Zhang's paper, the well-definedness of guts is general, and does not need the manifold to have non-degenerate Thurston norm. According to JSJ-theory, I-bundles and $S^1$-pairs $(S,T)$ contain all essential annuli and tori, where $S$ is a Seifert manifold and $T\subset \partial S$ is union of fibers. To define guts, we should continue cutting essential annuli $(A,\partial A)\subset (S,T)$, finally we get an I-bundle and some solid tori (containing singular fibers as core) with suture on the boundary. That's the picture in my head now. | |
| Feb 21 at 11:18 | comment | added | Sam Nead | I've edited my answer to more directly address the (lack of) Seifert fibered pieces. Previously I was not using the hypotheses correctly. | |
| Feb 21 at 11:14 | history | edited | Sam Nead | CC BY-SA 4.0 |
Ok, perhaps now??
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| Feb 21 at 11:06 | history | edited | Sam Nead | CC BY-SA 4.0 |
fixed math problem
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| Feb 21 at 9:25 | comment | added | Fredy | Why not decompose the Seifert manifolds? They may contain essential annuli as well, I thought we had to cut along those annuli to result in an I-bundle (which we throw away) and some solid torus with sutures on the boundary (which we keep as guts), for example, let M be a Seifert manifold with two sutures on the boundary, such that the two sutures are parallel to the fiber of M, it contains non-trivial guts, right? | |
| Feb 21 at 8:41 | comment | added | Sam Nead | For a general reference on sutured manifold theory, I recommend Martin Scharlemann’s articles “Lectures on the theory of sutured 3-manifolds” and (the much longer) “Sutured manifolds and generalised Thurston norms”. | |
| Feb 21 at 8:38 | comment | added | Sam Nead | We do not decompose the Seifert fibered spaces. Instead we throw them away. | |
| Feb 20 at 10:37 | comment | added | Fredy | I have more questions to Answer 1: the characteristic pair theorem gives Seifert submanifolds and I-bundles. The Seifert submanifolds contain annuli as well. should I further decompose the Seifert submanifolds along annuli to produce I-bundles and solid tori with sutures? Is there any reference for this argument? | |
| Feb 19 at 21:29 | history | answered | Sam Nead | CC BY-SA 4.0 |