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.

arXiv comment66 pages, several changes, some consequences added

References in corpus (9)

• Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces
• Surface group representations in PU(p,q) and Higgs bundles
• Deformations of maximal representations in Sp(4,R)
• Representations of the fundamental group of a closed oriented surface in Sp(4,R)
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• Quasi-Fuchsian AdS representations are Anosov
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Cited by in corpus (24)

• Anosov representations: Domains of discontinuity and applications
• Deformations of maximal representations in Sp(4,R)
• 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
• 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
• Nearly geodesic immersions and domains of discontinuity
• Cataclysms for Anosov representations
• Various generalizations and deformations of $PSL(2,\mathbb{R})$ surface group representations and their Higgs bundles
• Fiber bundles associated with Anosov representations
• Hitchin Pairs for non-compact real Lie groups
• A note on Reidemeister Torsion of G-Anosov Representations