Model Higgs Bundles in Exceptional Components of the Sp(4,R)-Character Variety

Authors

  • Georgios Kydonakis University of Illinois at Urbana-Champaign

DOI:

https://doi.org/10.24297/jam.v14i2.7444

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 alsoallows a comparison between the invariants for maximal Higgs bundles and the topological invariants for Anosov representations constructed by O. Guichard and A. Wienhard.

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Published

2018-06-27

How to Cite

Kydonakis, G. (2018). Model Higgs Bundles in Exceptional Components of the Sp(4,R)-Character Variety. JOURNAL OF ADVANCES IN MATHEMATICS, 14(2), 7744–7786. https://doi.org/10.24297/jam.v14i2.7444