ON THE IDEAL TRIANGULATION GRAPH OF A PUNCTURED SURFACE

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KORKMAZ M., Papadopoulos A.

ANNALES DE L INSTITUT FOURIER, cilt.62, sa.4, ss.1367-1382, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 62 Sayı: 4
  • Basım Tarihi: 2012
  • Doi Numarası: 10.5802/aif.2725
  • Dergi Adı: ANNALES DE L INSTITUT FOURIER
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1367-1382
  • Anahtar Kelimeler: mapping class group, surface, arc complex, ideal triangulation, ideal triangulation graph, curve complex, Gromov hyperbolic, AUTOMORPHISMS, COMPLEX, CURVES
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.