Earthquakes on Riemann surfaces and on measured geodesic laminations

Bonahon, Francis

doi:10.1090/S0002-9947-1992-1049611-3

Earthquakes on Riemann surfaces and on measured geodesic laminations
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by Francis Bonahon

Trans. Amer. Math. Soc. 330 (1992), 69-95

DOI: https://doi.org/10.1090/S0002-9947-1992-1049611-3

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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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