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2016 | OriginalPaper | Chapter

Higgs Bundles and Characteristic Classes

Author : Nigel Hitchin

Published in: Arbeitstagung Bonn 2013

Publisher: Springer International Publishing

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Abstract

Sixty years ago Hirzebruch observed how the vanishing of the Stiefel–Whitney class w 2 led to integrality of the \(\hat{A}\)-genus of an algebraic variety [Hirz1]. This was one motivation for the Atiyah–Singer index theorem but also for my own thesis about Dirac operators and Kähler manifolds. Indeed the interaction between topology and algebraic geometry which he developed has been a constant theme in virtually all my work.

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Literature
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[AGH]
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[GGM]
go back to reference O. Garcia-Prada, P. Gothen, I. Mundet i Riera, Higgs bundles and surface group representations in the real symplectic group. J. Topol. 6, 64–118 (2013) O. Garcia-Prada, P. Gothen, I. Mundet i Riera, Higgs bundles and surface group representations in the real symplectic group. J. Topol. 6, 64–118 (2013)
[Hit5]
go back to reference N.J. Hitchin, The Dirac operator, in Invitations to Geometry and Topology, ed. by M. Bridson, S. Salamon. Oxford Graduate Texts in Mathematics (Oxford University Press, Oxford, 2002), pp. 208–232 N.J. Hitchin, The Dirac operator, in Invitations to Geometry and Topology, ed. by M. Bridson, S. Salamon. Oxford Graduate Texts in Mathematics (Oxford University Press, Oxford, 2002), pp. 208–232
[LS]
go back to reference L.P. Schaposnik, Spectral data for G-Higgs bundles. D. Phil Thesis, Oxford (2013) L.P. Schaposnik, Spectral data for G-Higgs bundles. D. Phil Thesis, Oxford (2013)
[LS1]
go back to reference L.P. Schaposnik, Spectral data for U(m, m)-Higgs bundles. Int. Math. Res. Not. (2014). doi:10.1093/imrn/rnu029 L.P. Schaposnik, Spectral data for U(m, m)-Higgs bundles. Int. Math. Res. Not. (2014). doi:10.1093/imrn/rnu029
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[PG]
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Metadata
Title
Higgs Bundles and Characteristic Classes
Author
Nigel Hitchin
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-43648-7_8

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