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Déformations des applications harmoniques tordues

Abstract : We study the deformations of twisted harmonic maps f with respect to a representation. After constructing a continuous "universal" twisted harmonic map, we give a construction of every first order deformation of f in terms of Hodge theory; we apply this result to the moduli space of reductive representations of a Kähler group, to show that the critical points of the energy functional E coincide with the monodromy representations of polarized complex variations of Hodge structure. We then proceed to second order deformations, where obstructions arise; we investigate the existence of such deformations, and give a method for constructing them, as well. Applying this to the energy functional as above, we prove (for every finitely presented group) that the energy functional is strictly pluri sub-harmonic on the moduli space of representations; assuming furthermore that the group is Kähler, we study the eigenvalues of the Hessian of E at critical points.
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Contributor : Marco Spinaci <>
Submitted on : Thursday, December 12, 2013 - 2:57:41 PM
Last modification on : Wednesday, November 4, 2020 - 1:56:06 PM
Long-term archiving on: : Thursday, March 13, 2014 - 6:50:10 AM


  • HAL Id : tel-00877310, version 2



Marco Spinaci. Déformations des applications harmoniques tordues. Autre. Université de Grenoble, 2013. Français. ⟨NNT : 2013GRENM032⟩. ⟨tel-00877310v2⟩



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