Topology of moduli spaces of free group representations in real reductive groups
-
Ana Casimiro
,
Carlos Florentino
Abstract
Let G be a real reductive algebraic group with maximal compact subgroup K, and let Fr be a rank r free group. We show that the space of closed orbits in Hom(Fr,G)/G admits a strong deformation retraction to the orbit space Hom(Fr,K)/K. In particular, all such spaces have the same homotopy type. We compute the Poincaré polynomials of these spaces for some low rank groups G, such as Sp(4,ℝ) and U(2,2). We also compare these real moduli spaces to the real points of the corresponding complex moduli spaces, and describe the geometry of many examples.
Funding source: FCT, Portugal
Award Identifier / Grant number: PTDC/MAT-GEO/0675/2012
Funding source: FCT, Portugal
Award Identifier / Grant number: PTDC/MAT/120411/2010
Funding source: U.S. National Science Foundation
Award Identifier / Grant number: DMS 1107452
Funding source: U.S. National Science Foundation
Award Identifier / Grant number: DMS 1107263
Funding source: U.S. National Science Foundation
Award Identifier / Grant number: DMS 1107367
Funding source: Simons Foundation
Award Identifier / Grant number: 245642
Funding source: U.S. National Science Foundation
Award Identifier / Grant number: DMS 1309376
Funding source: Centro de Matemática da Universidade de Trás-os-Montes e Alto Douro
Award Identifier / Grant number: PEst-OE/MAT/UI4080/2011
We thank Tom Baird for many conversations about equivariant cohomology and Theorem 5.2. We also thank the referee for a careful reading, and for many suggestions leading to relevant improvements in exposition.
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Ring class invariants over imaginary quadratic fields
- The structure of p-local compact groups of rank 1
- Sampling and interpolation on some nilpotent Lie groups
- Topology of moduli spaces of free group representations in real reductive groups
- Finite symmetries of S4
- Variations of Minkowski's theorem on successive minima
- A one-relator group with long lower central series
- On transfinite nilpotence of the Vogel–Levine localization
- Time inhomogeneous generalized Mehler semigroups and skew convolution equations
- Specifying the Auslander–Reiten translation for complexes of modules
- Second order elliptic operators with diffusion coefficients growing as |x|α at infinity
- On the fourth derivative test for exponential sums
Articles in the same Issue
- Frontmatter
- Ring class invariants over imaginary quadratic fields
- The structure of p-local compact groups of rank 1
- Sampling and interpolation on some nilpotent Lie groups
- Topology of moduli spaces of free group representations in real reductive groups
- Finite symmetries of S4
- Variations of Minkowski's theorem on successive minima
- A one-relator group with long lower central series
- On transfinite nilpotence of the Vogel–Levine localization
- Time inhomogeneous generalized Mehler semigroups and skew convolution equations
- Specifying the Auslander–Reiten translation for complexes of modules
- Second order elliptic operators with diffusion coefficients growing as |x|α at infinity
- On the fourth derivative test for exponential sums
