Convergence of quasifuchsian hyperbolic 3-manifolds
Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015
Location: SLMath: Eisenbud Auditorium
hyperbolic manifold
hyperbolic group
asymptotic geometry
Bers' theorem
00A35 - Methodology of mathematics {For mathematics education, see 97-XX}
35R02 - PDEs on graphs and networks (ramified or polygonal spaces)
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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.)
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