Singularities of free group character varieties

Details Singularities of free group character varieties Singularities of free group character varieties

2009-07-27

arxiv.org/abs/0907.4720v3

Mathematics

Algebraic Geometry

38 pages. Version 3 adds references, minor corrections, revisions

Scientific paper

Let X be the moduli space of SL(n,C), SU(n), GL(n,C), or U(n)-valued representations of a rank r free group. We compute the fundamental group of X and show that these four moduli spaces have identical higher homotopy groups. We then classify the singular stratification of X. This comes down to showing that the singular locus corresponds exactly to reducible representations if there exist singularities at all. Lastly, we show that the moduli spaces X are generally not topological manifolds, except for a few examples we explicitly describe.

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