The topology of moduli spaces of free group representations

By C. Florentino, Sean Lawton. 2008

50 citations recorded by the source corpus.

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 $${{\rm SLm}(3, mathbb {C})}$$-character variety of a rank 2 free group is homotopic to an 8 sphere and the $${{\rm SLm}(2, mathbb {C})}$$-character variety of a rank 3 free group is homotopic to a 6 sphere.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1a9903ed85a2dbef49f5f9b69acf1092c391e589

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In Geometry and Topology

1. C. Florentino
2. William M. Goldman
3. Sean Lawton
4. Tudor Dimofte
5. Sergei Gukov
6. Ludovic Marquis

In Mathematical Physics

1. C. Florentino
2. William M. Goldman
3. Sean Lawton
4. Sergei Gukov
5. Tudor Dimofte
6. Ludovic Marquis

Citations in the corpus

• Locally Homogeneous Geometric Manifolds (2010, background): “Recently Florentino and Lawton [58] have determined the homotopy type of Hom(Γ, G)//G when Γ is free and G is a complex reductive group.”
• Topology of character varieties of Abelian groups (2013, background): “mmetric Yang-Mills theory and mirror symmetry ([7, 28, 47, 48]). Some special cases of this problem and related questions have recently received attention as can be seen, for example, in the articles [1, 4, 5, 16, 22, 36, 42]. Let Kbe a compact Lie group and view the Z-module Zr as a free Abelian gr”