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arXiv · 1509.02052

On the Narasimhan-Seshadri correspondence for Real and Quaternionic vector bundles

Florent Schaffhauser
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Abstract

Let E be a Real or Quaternionic Hermitian vector bundle over a Klein surface M. We study the action of the gauge group of E on the space of Galois-invariant unitary connections and we show that the closure of a semi-stable orbit contains a unique unitary orbit of projectively flat, Galois-invariant connections. We then use this invariant-theoretic perspective to prove a version of the Narasimhan-Seshadri correspondence in this context: S-equivalence classes of semi-stable Real and Quaternionic vector bundes are in bijective correspondence with equivalence classes of certain appropriate representations of orbifold fundamental groups of Real Seifert manifolds over the Klein surface M.

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Florent Schaffhauser. 2015-09-07. On the Narasimhan-Seshadri correspondence for Real and Quaternionic vector bundles. https://doi.org/10.4310/jdg%2F1483655861

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