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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The grafting map of Teichmüller space
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by Kevin P. Scannell and Michael Wolf PDF
J. Amer. Math. Soc. 15 (2002), 893-927 Request permission

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
  • MR Author ID: 184085
  • Email: mwolf@math.rice.edu
  • 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
  • © Copyright 2002 American Mathematical Society
  • 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
  • MathSciNet review: 1915822