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A geometric approach to orthogonal Higgs bundles


We give a geometric characterisation of the topological invariants associated to -Higgs bundles through KO-theory and the Langlands correspondence between orthogonal and symplectic Hitchin systems. By defining the split orthogonal spectral data, we obtain geometric description of the intersection of the moduli space of those Higgs bundles with the -Hitchin fibration in terms of a collection of compact abelian varieties, and provide a natural stratification of the moduli space of -Higgs bundles.

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This research was inspired by fruitful conversations with David Baraglia, Steve Bradlow and Nigel Hitchin. The author is also thankful for discussions with Ben Davidson and Alan Thompson, and for useful suggestions from the referee.

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Correspondence to Laura P. Schaposnik.

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The paper was written with partial support of the U.S. National Science Foundation Grants DMS 1107452, 1107263, 1107367: the GEAR Network for short research visits. The work of the author is also supported by NSF Grant DMS-1509693 and by the Alexander von Humboldt Foundation.

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Schaposnik, L.P. A geometric approach to orthogonal Higgs bundles. European Journal of Mathematics 4, 1390–1411 (2018).

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