✦ LIBER ✦

Profinite Teichmüller theory

✍ Scribed by Marco Boggi

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 471 KB
Volume: 279
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200510405

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✦ Synopsis

Abstract

For 2__g__ – 2 + n > 0, let Γ~g, n~ be the Teichmüller group of a compact Riemann surface of genus g with n points removed S~g, n~ , i.e., the group of homotopy classes of diffeomorphisms of S~g, n~ which preserve the orientation of S~g, n~ and a given order of its punctures. There is a natural faithful representation Γ~g, n~ → Out(π ~1~(S~g, n~ )). For any given finite index subgroup Γ^λ^ of Γ~g, n~ , the congruence subgroup problem asks whether there exists a finite index characteristic subgroup K of π ~1~(S~g, n~ ) such that the kernel of the induced representation Γ~g, n~ → Out(π ~1~(S~g, n~ )/K ) is contained in Γ^λ^ . The main result of the paper is an affirmative answer to this question. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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