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

Date

1999-07-01

Author

Korkmaz, Mustafa

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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.

URI

https://hdl.handle.net/11511/88719

Journal

TOPOLOGY AND ITS APPLICATIONS

DOI

https://doi.org/10.1016/s0166-8641(97)00278-2

Collections

Department of Mathematics, Article

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Citation Formats

M. Korkmaz, “Automorphisms of complexes of curves on punctured spheres and on punctured tori,” TOPOLOGY AND ITS APPLICATIONS, pp. 85–111, 1999, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/88719.