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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Earthquakes on Riemann surfaces and on measured geodesic laminations
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by Francis Bonahon PDF
Trans. Amer. Math. Soc. 330 (1992), 69-95 Request permission

Abstract:

Let $S$ be a closed orientable surface of genus at least $2$. We study properties of its Teichmüller space $\mathcal {T}(S)$, namely of the space of isotopy classes of conformal structures on $S$. W. P. Thurston introduced a certain compactification of $\mathcal {T}(S)$ by what he called the space of projective measured geodesic laminations. He also introduced some transformations of Teichmüller space, called earthquakes, which are intimately related to the geometry of $\mathcal {T}(S)$. A general problem is to understand which geometric properties of Teichmüller space subsist at infinity, on Thurston’s boundary. In particular, it is natural to ask whether earthquakes continuously extend at certain points of Thurston’s boundary, and at precisely which points they do so. This is the principal question addressed in this paper.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 330 (1992), 69-95
  • MSC: Primary 57N05; Secondary 32G15, 57R30, 58F17
  • DOI: https://doi.org/10.1090/S0002-9947-1992-1049611-3
  • MathSciNet review: 1049611