Character varieties for open surfaces.

Palestras e Seminários

03/12/2018

15:30

auditório Luiz Antonio Favaro (sala 4-111)

Palestrante: Julien Korinman

Responsável: Igor Mancattini (igorre@icmc.usp.br)

Seminário

Resumo: Given an oriented closed surface and an affine solvable Lie group G, the character variety is the moduli space of flat connections over a G-bundle over the surface. It is an affine symplectic variety with singularities. Character varieties first appeared in the work of Culler and Schalen on essential surfaces of 3-manifolds and attracted the attention of physicists and topologists for its relation with Chern-Simons topological quantum field theory and low dimensional topology. Geometers got involved in its study as well as these moduli spaces can be thought of as a generalization of the Teichmüller space of surfaces.

In this talk, I will present the basic definitions and properties of character varieties and propose a generalization for open surfaces. The main motivation for this new definition lies in the fact that these character varieties have a nice gluing property when we glue two surfaces along part of their boundary. I will also present the notion of quantization of Poisson varieties and show how skein theory provides natural quantizations of these moduli spaces. If time permits, I might present some applications in low-dimensional topology. This is a joint work with A.Quesney.

Also see

Character varieties for open surfaces.

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