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A faithful polynomial representation of Out F3

Published online by Cambridge University Press:  28 June 2011

James McCool
James McCool
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1
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Extract

Let Fn be a free group of rank n and let Out Fn be its outer automorphism group. The main result of this paper is that Out F3 has a faithful representation as a group of automorphisms of the polynomial ring in seven variables over the integers. This extends a similar result for n = 2 (see Helling [3], Horowitz [5] and Rosenberger [12]), and provides a partial answer to a conjecture attributed in [5] to W. Magnus. As an application of the special nature of the representing polynomials, we obtain our second result, that Out F3 is virtually residually torsion-free nilpotent.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 2 , September 1989 , pp. 207 - 213
Copyright
Copyright © Cambridge Philosophical Society 1989

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