Automorphisms of complexes of curves on punctured spheres and on punctured tori


TOPOLOGY AND ITS APPLICATIONS, cilt.95, sa.2, ss.85-111, 1999 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 95 Konu: 2
  • Basım Tarihi: 1999
  • Doi Numarası: 10.1016/s0166-8641(97)00278-2
  • Sayfa Sayıları: ss.85-111


Let S be either a sphere with greater than or equal to 5 punctures or a torus with greater than or equal to 3 punctures. We prove that the automorphism group of the complex of curves of S is isomorphic to the extended mapping class group M-S*. As applications we prove that surfaces of genus less than or equal to 1 are determined by their complexes of curves, and any isomorphism between two subgroups of M-S(*) of finite index is the restriction of an inner automorphism of M-S(*) We conclude that the outer automorphism group of a finite index subgroup of M-S(*) is finite, extending the fact that the outer automorphism group of M-S(*) is finite. For surfaces of genus greater than or equal to 2, corresponding results were proved by Ivanov (MES/M/89/60, Preprint). (C) 1999 Elsevier Science B.V. All rights reserved.