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Topics in Teichmuller Theory and Kleinian Groups |
| November 12, 2007 to November 16, 2007 |
| Organized By: Jeff Brock, Ken Bromberg, Richard Canary, Howard Masur, Alan Reid, Maryam Mirzakhani, and John Smillie |
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| Parent Programs: |
| Teichmuller Theory and Kleinian Groups |
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| Return to Workshop Description |
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Pants in 3-manifolds
Thursday November 15, 2007
02:00PM - 03:00PM
Speakers:
Ian Agol
Abstract:
We'll discuss pants (thrice punctured spheres) in
hyperbolic 3-manifolds.
We show that the simple loop conjecture holds for
pants. A proper map of a pants to a hyperbolic
3-manifold which is essential on embedded
simple closed curves and arcs is pi_1-injective
(in fact, by showing that it is totally geodesic).
We show that embedded pants are detected by ideal
points of the character variety.
We show that if a hyperbolic 3-manifold contains
an immersed pants, then it is obtained by Dehn
filling on one component of the Whitehead link
complement, and the immersed pants has a single
clasp, i.e. a single arc of double points.
We'll also describe related results of Shawn
Rafalski about immersed turnovers. An immersed
turnover in a hyperbolic orbifold
is contained in a canonical ``turnover core",
which is an embedded suborbifold with turnover
boundary and bounded volume. This is an analogue
of the JSJ decomposition for 3-manifolds.
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