# 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: McMullen_ComplexEarthquakes.pdf (522.0Kb; PDF) 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 Downloads of this work: