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The grafting map of Teichmüller space


Authors: Kevin P. Scannell and Michael Wolf
Journal: J. Amer. Math. Soc. 15 (2002), 893-927
MSC (2000): Primary 32G15; Secondary 30F10, 30F40, 30F60, 53C43, 57M50
DOI: https://doi.org/10.1090/S0894-0347-02-00395-8
Published electronically: May 16, 2002
MathSciNet review: 1915822
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Abstract: Grafting is a method of obtaining new projective structures from a hyperbolic structure, basically by gluing a flat cylinder into a surface along a closed geodesic in the hyperbolic structure, or by limits of that procedure. This induces a map of Teichmüller space to itself. We prove that this map is a homeomorphism by analyzing harmonic maps between pairs of grafted surfaces. As a corollary we obtain bending coordinates for the Bers embedding of Teichmüller space.


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Additional Information

Kevin P. Scannell
Affiliation: Department of Mathematics and Computer Science, Saint Louis University, Saint Louis, Missouri 63103
Email: scannell@slu.edu

Michael Wolf
Affiliation: Department of Mathematics, Rice University, Houston, Texas 77251
Email: mwolf@math.rice.edu

DOI: https://doi.org/10.1090/S0894-0347-02-00395-8
Received by editor(s): January 4, 2001
Received by editor(s) in revised form: January 18, 2002
Published electronically: May 16, 2002
Additional Notes: The second author was partially supported by NSF Grants DMS 9626565, DMS 9707770, (SCREMS) DMS 9971563
Article copyright: © Copyright 2002 American Mathematical Society

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