Singularities of free group character varieties

By C. Florentino, Sean Lawton. 2009

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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 spacesXr generally are not topological manifolds, except for a few examples we explicitly describe.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8925f7851ff0440e4dbd71516113ccdcd018209b