On the ideal triangulation graph of a punctured surface
Geometric Topology
2009-10-13 v1
Abstract
We study the ideal triangulation graph of a punctured surface of finite type. We show that if 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 into the simplicial automorphism group of is an isomorphism. We also show that under the same conditions on , the graph equipped with its natural simplicial metric is not Gromov hyperbolic. Thus, from the point of view of Gromov hyperbolicity, the situation of is different from that of the curve complex of .
Keywords
Cite
@article{arxiv.0910.2088,
title = {On the ideal triangulation graph of a punctured surface},
author = {Mustafa Korkmaz and Athanase Papadopoulos},
journal= {arXiv preprint arXiv:0910.2088},
year = {2009}
}