The topology of moduli spaces of free group representations

Details The topology of moduli spaces of free group representations The topology of moduli spaces of free group representations

2008-07-21

arxiv.org/abs/0807.3317v2

Mathematische Annalen 345 (2009), no. 2, 453-489

Mathematics

General Topology

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

Scientific paper

10.1007/s00208-009-0362-4

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.

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