Deformations of maximal representations in Sp(4,R)

Abstract

We use Higgs bundles to answer the following question: When can a maximal Sp(4,R)-representation of a surface group be deformed to a representation which factors through a proper reductive subgroup of Sp(4,R)?

49 pages; v2: various improvements and minor corrections; v3: improved exposition

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
• The Hitchin-Kobayashi correspondence, Higgs pairs and surface group representations
• Higgs bundles and surface group representations in the real symplectic group
• Topological Invariants of Anosov Representations
• Bounded Cohomology and Geometry
• Representations of the fundamental group of a closed oriented surface in Sp(4,R)
• Representations of surface groups in the projective general linear group
• Tight homomorphisms and Hermitian symmetric spaces

Cited by in corpus (20)

• Topological Invariants of Anosov Representations
• The geometry of maximal representations of surface groups into SO(2,n)
• Higher Teichmüller Spaces: from SL(2,R) to other Lie groups
• An Introduction to Higgs Bundles via Harmonic Maps
• Higgs bundles, the Toledo invariant and the Cayley correspondence
• Anosov representations with Lipschitz limit set
• The geometry of maximal components of the PSp(4,R) character variety
• Higgs bundles for the non-compact dual of the special orthogonal group
• Higgs bundles and higher Teichmüller spaces
• Maximal Sp(4,R) surface group representations, minimal immersions and cyclic surfaces
• SO(n,n+1)-surface group representations and their Higgs bundles
• Hitchin harmonic maps are immersions
• Higgs bundles and the real symplectic group
• Twisted cyclic quiver varieties on curves
• Nearly geodesic immersions and domains of discontinuity
• Morse Theory, Higgs fields and Yang-Mills-Higgs functionals
• Model Higgs bundles in exceptional components of the $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-character variety
• Fiber bundles associated with Anosov representations
• Boundary of the Gothen components
• Various generalizations and deformations of $PSL(2,\mathbb{R})$ surface group representations and their Higgs bundles