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Article Dans Une Revue Annales Henri Lebesgue Année : 2020

Holomorphic volume forms on representation varieties of surfaces with boundary

Résumé

For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality between two volume forms on the space of representations of the surface in a semisimple Lie group. One of the forms is a Reidemeister torsion, the other one is the power of the Atiyah-Bott-Goldman symplectic form. We introduce an holomorphic volume form on the space of representations of the circle, so that, for surfaces with boundary, it appears as peripheral term in the generalization of Witten's formula. We compute explicit volume and symplectic forms for some simple surfaces and for the Lie group SL(N,C).
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Dates et versions

hal-01770366 , version 1 (18-04-2018)
hal-01770366 , version 2 (27-10-2020)

Identifiants

Citer

Michael Heusener, Joan Porti. Holomorphic volume forms on representation varieties of surfaces with boundary. Annales Henri Lebesgue, 2020, 3, pp.341-380. ⟨10.5802/ahl.35⟩. ⟨hal-01770366v2⟩
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