Hitchin's equations on a nonorientable manifold

Research output: Contribution to journalArticlepeer-review

Full text download(s)

Published copy (DOI)



Publication details

JournalCommunications in Analysis and Geometry
DatePublished - 6 Sep 2018
Issue number4
Pages (from-to)857-886
Original languageEnglish


We define Hitchin’s moduli space for a principal bundle P, whose structure group is a compact semisimple Lie group K, over a compact non-orientable Riemannian manifold M. We use the Donaldson–Corlette correspondence, which identifies Hitchin’s moduli space with the moduli space of flat connections, which remains valid when M is non-orientable. This enables us to study Hitchin’s moduli space both by gauge theoretical methods and algebraically by using representation varieties. If the orientable double cover M~ of M is a Kähler manifold with odd complex dimension and if the Kähler form is odd under the non-trivial deck transformation τ on M~, Hitchin’s moduli space of the pull-back bundle has a hyper-Kähler structure and admits an involution induced by τ. The fixed-point set is symplectic or Lagrangian with respect to various symplectic structures on the moduli space. We compare the gauge theoretical constructions with the algebraic approach using representation varieties.

Bibliographical note

This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

Discover related content

Find related publications, people, projects, datasets and more using interactive charts.

View graph of relations