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Linear Representations of the Automorphism Group of a Free Group

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Abstract.

Let F n be the free group on n ≥ 2 elements and Aut(F n ) its group of automorphisms. In this paper we present a rich collection of linear representations of Aut(F n ) arising through the action of finite-index subgroups of it on relation modules of finite quotient groups of F n . We show (under certain conditions) that the images of our representations are arithmetic groups.

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Authors and Affiliations

  1. Mathematisches Institut, Heinrich-Heine-Universität, D-40225, Düsseldorf, Germany

    Fritz Grunewald

  2. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Alexander Lubotzky

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  1. Fritz Grunewald
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  2. Alexander Lubotzky
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Correspondence to Fritz Grunewald.

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Received: November 2006, Accepted: March 2007

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Grunewald, F., Lubotzky, A. Linear Representations of the Automorphism Group of a Free Group. GAFA Geom. funct. anal. 18, 1564–1608 (2009). https://doi.org/10.1007/s00039-009-0702-2

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  • DOI: https://doi.org/10.1007/s00039-009-0702-2

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