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

• 成果类型: Article
• 署名作者: Aparicio-Arroyo, Marta; Bradlow, Steven; Collier, Brian; Garcia-Prada, Oscar; Gothen, Peter B.; Oliveira, Andre
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University System of Maryland; University of Maryland College Park; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); Universidade do Porto; University of Tras-os-Montes & Alto Douro
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00885-2
• 发表日期: 2019
• 页码: 197-299
• 关键词: surface group-representations; higgs bundles; MODULI SPACES; CONNECTEDNESS; systems; pairs

摘要

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 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).