Singularities of free group character varieties

Abstract

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 classify the algebraic singular stratification of X. 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 X generally are not topological manifolds, except for a few examples we explicitly describe.

33 pages. Version 4 is shorter and more focused; cut material will be expanded upon and written up in subsequent papers. Clarifications, and expository revisions have been added. Accepted for publication in Pacific Journal of Mathematics

References in corpus (3)

• Generators, Relations and Symmetries in Pairs of 3x3 Unimodular Matrices
• The topology of moduli spaces of free group representations
• The variety of characters in PSL(2,C)

Cited by in corpus (25)

• E-polynomial of the SL(3,C)-character variety of free groups
• Topology of Moduli Spaces of Free Group Representations in Real Reductive Groups
• Homotopy Groups of Free Group Character Varieties
• Decision problems, complexity, traces, and representations
• Serre polynomials of $S{L}_n$- and $PG{L}_n$-character varieties of free groups
• E-polynomial of SL(2,C)-Character Varieties of Free groups
• Varieties of Characters
• Character Varieties of Free Groups are Gorenstein but not always Factorial
• Symplectic resolutions of character varieties
• Invariants of pairs in SL(4,C) and SU(3,1)
• Motive of the $S{L}_4$-character variety of torus knots
• Flawed groups and the topology of character varieties
• Representation variety for the rank one affine group
• G-Character varieties for G=SO(n,C) and other not simply connected groups
• Representation varieties of twisted Hopf links
• Generating series for the $E$-polynomials of $GL(n,\mathbb{C})$-character varieties
• Bad Representations and Homotopy of Character Varieties
• Bad irreducible subgroups and singular locus for character varieties in $PSL(p,\mathbb{C})$
• Conditions of smoothness of moduli spaces of flat connections and of character varieties
• Mixed Hodge structures on character varieties of nilpotent groups
• Character Varieties of Generalized Torus Knot Groups
• Dynamics on the SU(2,1)-character variety of the one-holed torus
• Centralizers of irreducible subgroups in the projective special linear group
• SO(2n,C)-character varieties are not varieties of characters
• Newton-Okounkov polyhedra for character varieties and configuration spaces