Topological Invariants of Anosov Representations

Abstract

We define new topological invariants for Anosov representations and study them in detail for maximal representations of the fundamental group of a closed oriented surface into the symplectic group.

66 pages, several changes, some consequences added

References in corpus (3)

• Surface group representations with maximal Toledo invariant
• Quasi-Fuchsian AdS representations are Anosov
• Three-dimensional Anosov flag manifolds

Cited by in corpus (23)

• Anosov representations: Domains of discontinuity and applications
• Higher Teichmüller Spaces: from SL(2,R) to other Lie groups
• Anosov representations with Lipschitz limit set
• The geometry of maximal components of the PSp(4,R) character variety
• SO(p,q)-Higgs bundles and higher Teichmüller components
• Higgs bundles for the non-compact dual of the special orthogonal group
• Affine Anosov representations and proper actions
• Maximal Sp(4,R) surface group representations, minimal immersions and cyclic surfaces
• Positive surface group representations in PO(p,q)
• SO(n,n+1)-surface group representations and their Higgs bundles
• A general Cayley correspondence and higher Teichmüller spaces
• Margulis Multiverse: Infinitesimal Rigidity, Pressure Form and Convexity
• Representations and geometric structures
• Positively ratioed representations
• Thurston's cataclysms for Anosov representations
• Cataclysms for Anosov representations
• Nearly geodesic immersions and domains of discontinuity
• Model Higgs bundles in exceptional components of the $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-character variety
• Maximal Higgs bundles for adjoint forms via Cayley correspondence
• Hitchin Pairs for non-compact real Lie groups
• Various generalizations and deformations of $PSL(2,\mathbb{R})$ surface group representations and their Higgs bundles
• A note on Reidemeister Torsion of G-Anosov Representations
• Fiber bundles associated with Anosov representations