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ON THE IDEAL TRIANGULATION GRAPH OF A PUNCTURED SURFACE
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Date
2012-01-01
Author
Korkmaz, Mustafa
Papadopoulos, Athanase
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This work is licensed under a
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We study the ideal triangulation graph T(S) of an oriented punctured surface S of finite type. We show that if S is not the sphere with at most three punctures or the torus with one puncture, then the natural map from the extended mapping class group of S into the simplicial automorphism group of T(S) is an isomorphism. We also show that, the graph T(S) of such a surface S. equipped with its natural simplicial metric is not Gromov hyperbolic. We also show that if the triangulation graph of two oriented punctured surfaces of finite type are homeomorphic, then the surfaces themselves are homeomorphic.
Subject Keywords
Mapping class group
,
Surface
,
Arc complex
,
Ideal triangulation graph
,
Curve complex
,
Gromov hyperbolic
URI
https://hdl.handle.net/11511/36334
Journal
ANNALES DE L INSTITUT FOURIER
DOI
https://doi.org/10.5802/aif.2725
Collections
Department of Mathematics, Article