Linear Representations of the Automorphism Group of a Free Group

By Fritz Grunewald, Alexander Lubotzky. 2006

83 citations recorded by the source corpus.

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

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dc621bf349c1c5ab6328e2b746c9af037b2a5261

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Automorphisms of graph products of groups from a geometric perspective (2018, background): “In the opposite direction, it is known that Aut(Fn) does not have property (T) for n = 2 and 3 [8, 23, 36]; that it has property (T) for n 5 by very recent results of [32, 33]; and the case n = 4 is still open.”
Arithmetic quotients of the mapping class group (2013, background): “Up to now, the above procedure follows that of [15] with the important exception that Grunewald and Lubotzky use the actual theorem of Gaschütz in place of Proposition 1.”