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

Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany

E-mail Address: kydonakis@mpim-bonn.mpg.de

https://doi.org/10.1142/S0129167X21500671Cited by:1 (Source: Crossref)

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 $2 g - 3$ exceptional components of the maximal $Sp (4, ℝ)$ -Higgs bundle moduli space, which correspond to components solely consisting 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 Guichard and Wienhard.

Communicated by Oscar Garcia-Prada

Keywords:

AMSC: 53C07, 14H60, 58D27

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