Homogeneous Dynamics and Anosov Representations: Bending, entropy and proper affine actions of surface groups
Presenter
April 24, 2026
Keywords:
- discrete subgroups
- semisimple Lie groups
- Anosov representations
- convex projective geometry
- entropy
- geometric structures
- Hitchin representations
- homogeneous dynamics
- mixing
- thermodynamic formalism
- thin subgroups
MSC:
- 20-XX - Group theory and generalizations
- 22-XX - Topological groups
- Lie groups
- 37-XX - Dynamical systems and ergodic theory
- 53-XX - Differential geometry
- 57-XX - Manifolds and cell complexes
Abstract
We study the variation of complex length with respect to bending deformations of quasifuchsian groups. As one application, we exhibit an explicit open neighborhood of the Fuchsian locus in quasifuchsian space so that the only critical points of the entropy function in this neighborhood lie on the Fuchsian locus. As a second application, we exhibit an explicit open neighborhood of the Fuchsian locus so that the adjoint of every representation which is not Fuchsian is the linear part of a proper affine action on the Lie algebra of SL(2,C).