Deformations of twisted harmonic maps
type: Dataset
description: 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.
identifier: NNT: 2013GRENM032
issued: 2026-05-07T20:11:29.281642
language: fr
modified: 2026-05-07T20:11:29.281647
contact point: Organization
  fn: CCSD
keyword: applications-harmoniques-tordues
keyword: energy-functional
keyword: espaces-de-modules
keyword: fibres-de-higgs
keyword: fonctionnelle-denergie
keyword: groupes-de-kahler
keyword: higgs-bundles
keyword: infoeu-reposemanticsdoctoralthesis
keyword: kahler-groups
keyword: moduli-spaces
keyword: spiotherengineering-sciences-physicsother
keyword: theses
keyword: twisted-harmonic-maps
keyword: variation-of-hodge-structures
keyword: variations-de-structures-de-hodge
landing page: https://theses.hal.science/tel-00877310

Deformations of twisted harmonic maps
type: Distribution
format: HTML
issued: 2026-05-07T20:11:29.298233
modified: 2026-05-07T20:11:29.266611
access URL: https://theses.hal.science/tel-00877310

test_moissonnage_selune
type: Agent