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Singularities of free
group character varieties
Carlos Florentino and Sean Lawton |
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Vol. 260 (2012), No. 1, 149–179
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Abstract |
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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. |
Keywords
character variety, singularities, local topology
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Mathematical Subject Classification 2010
Primary: 14B05, 32S05
Secondary: 14L30, 20CXX, 14P10
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Milestones
Received: 30 May 2012
Accepted: 16 June 2012
Published: 11 October 2012
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Authors |
| Carlos Florentino | |
| Departamento de Matemática Instituto Superior Técnico 1049-001 Lisboa Portugal |
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| Sean Lawton | |
| Department of Mathematics University of Texas-Pan American 1201 West University Drive Edinburg, TX 78539 United States |
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