The (asymptotic) location of eigenvalues of a representation in the Hitchin component
Presenter
April 13, 2015
Keywords:
- Riemann surfaces
- mapping class groups
- co-compact group action
- discrete group of isometries
- Hausdorff dimension
- entropy
- quasi-Fuchsian group
MSC:
- 53D18
- 53Dxx
- 53-xx
- 30Fxx
- 30F25
- 30F35
- 30F60
- 32G15
Abstract
The Hitchin component is a (special) connected component of the space of homomorphisms of a surface group into $\textrm{PSL}(d,\mathbb{R}).$ This component is a higher rank analogue of the Teichmuller space of the surface. The purpose of the talk is to show that the critical exponent of a Hitchin representation has a rigid upper bound. This is a joint work with Rafael Potrie.