The topology of moduli spaces of free group representations

Abstract

For any complex affine reductive group G and a fixed choice of maximal compact subgroup K, we show that the G-character variety of a free group strongly deformation retracts to the corresponding K-character space, which is a real semi-algebraic set. Combining this with constructive invariant theory and classical topological methods, we show that the SL(3,C)-character variety of a rank 2 free group is homotopic to an 8 sphere and the SL(2,C)-character variety of a rank 3 free group is homotopic to a 6 sphere.

37 pages, 2 figures, version 2 corrects typos, generalizes context, and adds a corollary, it is the accepted version to appear in Mathematische Annalen

References in corpus (2)

• Poisson Geometry of SL(3,C)-Character Varieties Relative to a Surface with Boundary
• Quantizations of Character Varieties and Quantum Knot Invariants

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• Non-ergodicity on SU(2) and SU(3) character varieties of the once-punctured torus
• On the types of the mixed Hodge structures of character varieties
• Dynamics on the SU(2,1)-character variety of the one-holed torus
• $e$-polynomials of character varieties