SO (p, q) -Higgs bundles and Higher Teichmüller components

Marta Aparicio-Arroyo, Steven Bradlow, Brian Collier, Oscar García-Prada, Peter B. Gothen, André Oliveira

Research output: Contribution to journalArticle

Abstract

Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such ‘exotic’ components in moduli spaces of SO (p, q) -Higgs bundles on closed Riemann surfaces or, equivalently, moduli spaces of surface group representations into the Lie group SO (p, q). Furthermore, we discuss how these exotic components are related to the notion of positive Anosov representations recently developed by Guichard and Wienhard. We also provide a complete count of the connected components of these moduli spaces (except for SO (2 , q) , with q⩾ 4).

Original languageEnglish (US)
Pages (from-to)197-299
Number of pages103
JournalInventiones Mathematicae
Volume218
Issue number1
DOIs
StatePublished - Oct 1 2019

ASJC Scopus subject areas

  • Mathematics(all)

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    Aparicio-Arroyo, M., Bradlow, S., Collier, B., García-Prada, O., Gothen, P. B., & Oliveira, A. (2019). SO (p, q) -Higgs bundles and Higher Teichmüller components. Inventiones Mathematicae, 218(1), 197-299. https://doi.org/10.1007/s00222-019-00885-2