On somes characteristic classes of flat bundles in complex geometry
Annales de l'Institut Fourier, Volume 69 (2019) no. 2, pp. 729-751.

On a compact Kähler manifold X, any semisimple flat bundle carries a harmonic metric. It can be used to define some characteristic classes of the flat bundle, in the cohomology of X. We show that these cohomology classes come from an infinite-dimensional space, constructed with loop groups, an analogue of the period domains used in Hodge theory.

Sur une variété kählérienne compacte X, tout fibré plat semi-simple admet une métrique harmonique. On peut grâce à elle définir certaines classes caractéristiques du fibré plat, dans la cohomologie de X. Nous montrons que ces classes de cohomologie proviennent d’un espace de dimension infinie construit à partir de groupes de lacets, cet espace étant un analogue des domaines de périodes de la théorie de Hodge.

Published online:
DOI: 10.5802/aif.3255
Classification: 57R20, 22E67, 58A14
Keywords: harmonic bundles, non-abelian Hodge theory, flat bundles, loop groups, period domains
Mot clés : fibrés harmoniques, théorie de Hodge non-abélienne, fibrés plats, groupes de lacets, domaines de périodes
Daniel, Jeremy 1

1 Max Planck Institute Bonn (Germany)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Daniel, Jeremy. On somes characteristic classes of flat bundles in complex geometry. Annales de l'Institut Fourier, Volume 69 (2019) no. 2, pp. 729-751. doi : 10.5802/aif.3255. https://aif.centre-mersenne.org/articles/10.5802/aif.3255/

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