Geodesic
The boundary at infinity of the curve complex and the relative Teichmüller space
Erica Klarreich1
1Berkeley, USA
Groups, geometry, and dynamics, Tome 16 (2022) no. 2, pp. 705-723

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DOI

In this paper we study the boundary at infinity of the curve complex C(S) of a surface S of finite type and the relative Teichmüller space Tel​(S) obtained from the Teichmüller space by collapsing each region where a simple closed curve is short to be a set of diameter 1. C(S) and Tel​(S) are quasi-isometric, and Masur–Minsky have shown that C(S) and Tel​(S) are hyperbolic in the sense of Gromov. We show that the boundary at infinity of C(S) and Tel​(S) is the space of topological equivalence classes of minimal foliations on S.
DOI : 10.4171/ggd/662
Classification : 57-XX, 20-XX, 30-XX, 32-XX
Mots-clés : Curve complex, boundary at infinity, relative Teichmüller space, measured foliation

Erica Klarreich  1

1 Berkeley, USA 
Erica Klarreich. The boundary at infinity of the curve complex and the relative Teichmüller space. Groups, geometry, and dynamics, Tome 16 (2022) no. 2, pp. 705-723. doi: 10.4171/ggd/662
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     title = {The boundary at infinity of the curve complex and the relative {Teichm\"uller} space},
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     pages = {705--723},
     year = {2022},
     volume = {16},
     number = {2},
     doi = {10.4171/ggd/662},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/662/}
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