Timeline for Geodesic cuffs of pairs of pants in a hyperbolic manifold- why are they disjoint?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 20, 2012 at 19:33 | comment | added | Ian Agol | @ Daniel: I think it's hidden in the statement of Theorem 3.1. The conditions on the pants guarantee that it's close to being totally geodesic, and therefore the cuffs don't intersect. | |
| Dec 20, 2012 at 7:48 | comment | added | Daniel Moskovich | Where do Kahn and Markovic guarantee no intersections between cuffs? I'm looking at the construction of $\delta$ in Section 4.5. Thank you for the explanation of "feet" when there are intersections! | |
| Dec 19, 2012 at 18:46 | comment | added | Ian Agol | @ Lee: Yes, the cuffs of a general pants could intersect each other, although the cuffs will themselves be embedded. However, Kahn & Markovic make sure that the cuffs don't intersect, and in fact the pants are very close to being totally geodesic (this requires some careful estimates to make sure this happens). | |
| Dec 19, 2012 at 18:32 | comment | added | Lee Mosher | One might also want to go all the way up to $\mathbb{H}^3$ and visualize the right-angled hexagons associated to $\rho(\pi_1(\Pi^0))$, although even in $\mathbb{H}^3$ there are cases where the hexagons degenerate to being non-embedded. | |
| Dec 19, 2012 at 18:08 | history | answered | Ian Agol | CC BY-SA 3.0 |