Vol. 260, No. 1, 2012

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Singularities of free group character varieties

Carlos Florentino and Sean Lawton

Vol. 260 (2012), No. 1, 149–179

Let Xr be the moduli space of SLn, SUn, GLn, or Un -valued representations of a rank r free group. We classify the algebraic singular stratification of Xr. This comes down to showing that the singular locus corresponds exactly to reducible representations if there exist singularities at all. Then by relating algebraic singularities to topological singularities, we show the moduli spaces Xr generally are not topological manifolds, except for a few examples we explicitly describe.

character variety, singularities, local topology
Mathematical Subject Classification 2010
Primary: 14B05, 32S05
Secondary: 14L30, 20CXX, 14P10
Received: 30 May 2012
Accepted: 16 June 2012
Published: 11 October 2012
Carlos Florentino
Departamento de Matemática
Instituto Superior Técnico
1049-001 Lisboa
Sean Lawton
Department of Mathematics
University of Texas-Pan American
1201 West University Drive
Edinburg, TX 78539
United States