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Exotic components of SO(p,q) surface group representations, and their Higgs bundle avatars

Preprint

<p>For semisimple Lie groups, moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. In many cases, natural topological invariants label connected components of the moduli spaces. Hitchin representations into split real forms, and maximal representations into Hermitian Lie groups, are the only previously know cases where natural invariants do not fully distinguish connected components. In this note we announce the existence of new such exotic components in the moduli spaces for the groups SO(<em>p</em>,<em>q</em>) with 2\&lt;<em>p</em>\&lt;<em>q</em>. These groups lie outside formerly know classes of groups associated with exotic components.</p>

Marta Aparicio-Arroyo

Steven Bradlow

Brian Colier

Oscar ia-Prada

Peter Gothen

Andr\ Oliveira

Publication

Year of publication: 2018

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