no. 2
On somes characteristic classes of flat bundles in complex geometry
Daniel, Jeremy1
1Max Planck Institute Bonn (Germany)
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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3255
Classification: 57R20, 22E67, 58A14
Keywords: harmonic bundles, non-abelian Hodge theory, flat bundles, loop groups, period domains
Mots-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
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
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