Topology Atlas | Conferences

Knots in Washington XVI; Conference on Knot Theory and its Ramifications
May 5-7, 2003
University of Maryland
College Park, MD, USA

Organizers
Marta M. Asaeda (UMD), William M. Goldman (UMD), John J. Millson (UMD), Jozef H. Przytycki (GWU)

Conference Homepage


Automorphisms of the Fricke characters of free groups
by
Richard Brown
American University

The set of all special linear characters of a Free group is an algebraic variety that can be realized as a subset of complex space cut out via a minimal set of polynomial manifestations of the Magnus Relation. Automorphisms of the free group induce automorphisms of this variety which preserve "volume" up to sign. We establish that these automorphisms extend to polynomial automorphisms of the ambient space which also preserve "volume" up to sign. When the free group is the fundamental group of a surface, this leads to a good algebriac model for the study of the dynamics of mapping class actions on surface character varieties.

Date received: April 30, 2003

Copyright © 2003 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # calc-10.