On somes characteristic classes of flat bundles in complex geometry
[Classes caractéristiques de fibrés plats en géométrie complexe]
Annales de l'Institut Fourier, Tome 69 (2019) no. 2, pp. 729-751.

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.

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.

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DOI : https://doi.org/10.5802/aif.3255
Classification : 57R20,  22E67,  58A14
Mots clés : fibrés harmoniques, théorie de Hodge non-abélienne, fibrés plats, groupes de lacets, domaines de périodes
@article{AIF_2019__69_2_729_0,
     author = {Daniel, Jeremy},
     title = {On somes characteristic classes of flat bundles in complex geometry},
     journal = {Annales de l'Institut Fourier},
     pages = {729--751},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {69},
     number = {2},
     year = {2019},
     doi = {10.5802/aif.3255},
     zbl = {07067416},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3255/}
}
Daniel, Jeremy. On somes characteristic classes of flat bundles in complex geometry. Annales de l'Institut Fourier, Tome 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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