Automorphisms of the Fricke characters of groups
| dc.creator | Brown, Richard | |
| dc.date | 2003-11-07 | |
| dc.date.accessioned | 2026-07-07T05:02:44Z | |
| dc.date.available | 2026-07-07T05:02:44Z | |
| dc.description | In this note, we embed the set of all Fricke characters of a free group F -- the set of all characters of representations of F into SL(2,C) -- as an irreducible affine variety V in complex affine space of dimension 2^n-1. Using the Horowitz generating set as the indeterminates, we show that the ideal I of all polynomials in these indeterminates which vanish on V is finitely generated by the Magnus relation for arbitrary octets of elements in SL(2,C). Using this relation, we produce a basis for I, and show that it is prime. We then show that the natural action of automorphisms of F on V extends to polynomial automorphisms on all of the ambient affine space which, up to sign, preserve a complex volume form. This construction provides an algebraic model for the analysis of the dynamics of the measure preserving action of Out(F) on V. | |
| dc.description | 17 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0311119 | |
| dc.identifier | http://arxiv.org/abs/math/0311119 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69121 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Dynamical Systems | |
| dc.subject | 57M05; 30F60; 20H10; 14J50 | |
| dc.title | Automorphisms of the Fricke characters of groups | |
| dc.type | text |