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
Other Sources: http://www.math.harvard.edu/~ctm/papers/index.html
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3445976

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  • FAS Scholarly Articles [7219]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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