The harmonic Magnus expansion on a compact Riemann surface with non-zero tangent vectors (Nariya Kawazumi, University of Tokyo)

14.11.2017 15:00

This talk is a review of my old preprint https://arxiv.org/abs/math/0603158. In order to study algebraic natures of the mapping class group for a compact surface, we often use group-like expansions of the fundamental group of the surface. There is no canonical group-like expansions associated with the topological structure of the surface, which is a raison d’etre of the Johnson homomorphisms. But there is a canonical group-like expansion associated with a complex structure on the surface. Generalizing B. Harris’ harmonic volume of a compact Riemann surface, we introduced such a canonical expansion in the preprint stated above, which we named the harmonic Magnus expansion.

This talk is divided into two 45 min talks. We will explain how to construct the expansion as the holonomy of a singular connection on the surface in Part I, and discuss discuss the first variation of the expansions as a flat connection on the Teichmueller space whose holonomy gives the Johnson homomorphisms in Part II.

Lieu

Bâtiment: Battelle

Séminaire "Groupes de Lie et espaces des modules"

Organisé par

Section de mathématiques

Intervenants

Nariya Kawazumi, University of Tokyo

entrée libre

Classement

Catégorie: Séminaire