Model Higgs bundles in exceptional components of the Sp(4,ℝ)-character variety

2018/05/26 by Georgios Kydonakis, Kydonakis, Georgios
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1805.10497

openalex publication_date 2018/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a gluing construction for Higgs bundles over a connected sum of Riemann surfaces in terms of solutions to the Sp(4,ℝ)-Hitchin equations using the linearization of a relevant elliptic operator. The construction can be used to provide model Higgs bundles in all the 2g-3 exceptional components of the maximal Sp(4,ℝ)-Higgs bundle moduli space, which correspond to components solely consisted of Zariski dense representations. This also allows a comparison between the invariants for maximal Higgs bundles and the topological invariants for Anosov representations constructed by O. Guichard and A. Wienhard.

Citations

• The Self-Duality Equations on a Riemann Surface
• The Beauville-Narasimhan-Ramanan correspondence for twisted Higgs V-bundles and components of parabolic Sp(2n,ℝ)-Higgs moduli Spaces

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