Timeline for Haken manifolds and characterising sutured manifold hierarchies
Current License: CC BY-SA 3.0
7 events
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| Aug 22, 2013 at 3:16 | comment | added | Ian Agol | In Theorem 1, the "Internal Hierarchy" may terminate in one of 6 possibilities, one of which is $T^2\times I$. But there is no hyperbolicity statement there. In Theorem 2, one interpolates between finite-volume hyperbolic manifolds, keeping everything hyperbolic in between. However, $T^2\times I$ does not have a finite-volume hyperbolic metric. So I'm confused which theorem you're referring to? | |
| Aug 15, 2013 at 5:59 | comment | added | Don Shanil | Yes, Having an angle structure is good enough for me. The motivation for the question is that I can construct a class of hierarchies for the manifold in question and was hoping to construct an angle structure using this (or at least to get some condition when this is possible). | |
| Aug 14, 2013 at 16:38 | comment | added | Scott Taylor | This is by no means an answer, but you might consider Lackenby's paper "Taut ideal triangulations" (G&T 2000). I believe there's a relationship between those triangulations and angle structures (if not actual hyperbolic structures) and by construction the taut ideal triangulation is constructed from taut id. triang. on the pieces at the end of the hierarchy. | |
| Aug 14, 2013 at 13:43 | history | edited | Don Shanil | CC BY-SA 3.0 |
Added condition
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| Aug 14, 2013 at 4:06 | comment | added | Don Shanil | Yes, I also assume that $M$ is atoroidal, thanks Neil for pointing that out. | |
| Aug 13, 2013 at 8:45 | comment | added | Neil Hoffman | Are you assuming that the interior of $M$ is atoroidal? | |
| Aug 13, 2013 at 7:08 | history | asked | Don Shanil | CC BY-SA 3.0 |