# On the ideal triangulation graph of a punctured surface

Mustafa Korkmaz^{[1]}; Athanase Papadopoulos^{[2]}

- [1] Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey.
- [2] Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany Institut de Recherche Mathématique Avancée, Université de Strasbourg and CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France.

Annales de l’institut Fourier (2012)

- Volume: 62, Issue: 4, page 1367-1382
- ISSN: 0373-0956

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topKorkmaz, Mustafa, and Papadopoulos, Athanase. "On the ideal triangulation graph of a punctured surface." Annales de l’institut Fourier 62.4 (2012): 1367-1382. <http://eudml.org/doc/251130>.

@article{Korkmaz2012,

abstract = {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.},

affiliation = {Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey.; Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany Institut de Recherche Mathématique Avancée, Université de Strasbourg and CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France.},

author = {Korkmaz, Mustafa, Papadopoulos, Athanase},

journal = {Annales de l’institut Fourier},

keywords = {mapping class group; surface; arc complex; ideal triangulation; ideal triangulation graph; curve complex; Gromov hyperbolic},

language = {eng},

number = {4},

pages = {1367-1382},

publisher = {Association des Annales de l’institut Fourier},

title = {On the ideal triangulation graph of a punctured surface},

url = {http://eudml.org/doc/251130},

volume = {62},

year = {2012},

}

TY - JOUR

AU - Korkmaz, Mustafa

AU - Papadopoulos, Athanase

TI - On the ideal triangulation graph of a punctured surface

JO - Annales de l’institut Fourier

PY - 2012

PB - Association des Annales de l’institut Fourier

VL - 62

IS - 4

SP - 1367

EP - 1382

AB - 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.

LA - eng

KW - mapping class group; surface; arc complex; ideal triangulation; ideal triangulation graph; curve complex; Gromov hyperbolic

UR - http://eudml.org/doc/251130

ER -

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