On somes characteristic classes of flat bundles in complex geometry
Annales de l'Institut Fourier, to appear, 23 p.

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 : 2017-09-06
Revised : 2018-02-06
Accepted : 2018-03-13
Classification:  57R20,  22E67,  58A14
Keywords: harmonic bundles, non-abelian Hodge theory, flat bundles, loop groups, period domains
     author = {Daniel, Jeremy},
     title = {On somes characteristic classes of flat bundles in complex geometry},
     note = {to appear in \emph{Annales de l'Institut Fourier}},
Daniel, Jeremy. On somes characteristic classes of flat bundles in complex geometry. Annales de l'Institut Fourier, to appear, 23 p.

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