Moduli spaces of flat connections on an oriented surface can be described by embedded graphs that are decorated with elements of Poisson-Lie groups. This can be viewed as a Poisson-Lie counterpart of Reshetikhin-Turaev TQFTs and is the starting point of combinatorial quantisation of moduli spaces. It was shown recently that Kitaev lattice models can be viewed as the Hamiltonian counterparts of Turaev-Viro TQFT, and a precise relation between Kitaev models and combinatorial quantisation was established. We define the Poisson-Lie analogue of Kitaev models and relate it to Fock and Rosly's description of moduli spaces of flat connections. This amounts to a Poisson-Lie version of the relation between Kitaev models and combinatorial quantisation.
Moduli spaces of flat connections and Poisson analouges of Kitaev models
18.06.2018 12:00 - 13:00
Organiser:
N. Carqueville
Location: