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# Convergence of quasifuchsian hyperbolic 3-manifolds

## Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015

April 13, 2015 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Richard Canary (University of Michigan)
Location: MSRI: Simons Auditorium
Tags/Keywords
• hyperbolic manifold

• hyperbolic group

• asymptotic geometry

• Bers' theorem

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

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Abstract

Thurston's Double Limit Theorem provided a criterion ensuring convergence, up to subsequence, of a sequence of quasifuchsian representations. This criterion was the key step in his proof that 3-manifolds which fiber over the circle are geometrizable.  In this talk, we describe a complete characterization of when a sequence of quasifuchsian representations has a convergent subsequence.  Moreover, we will see that the asymptotic behavior of the conformal structures determines the ending laminations and parabolic loci of the algebraic limit and how the algebraic limit wraps'' inside the geometric limit. (The results described are joint work with Jeff Brock, Ken Bromberg, Cyril Lecuire and Yair Minsky.)

Video/Audio Files

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