Complex Earthquakes and Teichmuller Theory

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Complex Earthquakes and Teichmuller Theory

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Title: Complex Earthquakes and Teichmuller Theory
Author: McMullen, Curtis T.
Citation: McMullen, Curtis T. 1998. Complex earthquakes and Teichmuller theory. Journal of the American Mathematical Society 11: 283–320. Revised 2005.
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Abstract: It is known that any two points in Teichmuller space are joined by an earthquake path. In this paper we show any earthquake path \(\mathbb{R} \rightarrow T(S)\) extends to a proper holomorphic mapping of a simplyconnected domain D into Teichmuller space, where \(\mathbb{R} ⊂ \mathbb{D} ⊂ \mathbb{C}\). These complex earthquakes relate Weil-Petersson geometry, projective structures, pleated surfaces and quasifuchsian groups. Using complex earthquakes, we prove grafting is a homeomorphism for all 1-dimensional Teichmuller spaces, and we construct bending coordinates on Bers slices and their generalizations. In the appendix we use projective surfaces to show the closure of quasifuchsian space is not a topological manifold.
Published Version: doi:10.1090/S0894-0347-98-00259-8
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