Complex Earthquakes and Teichmuller Theory
| 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. |
| Full Text & Related Files: |
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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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