On topologies on Lie braid groups

TL;DR

This paper explores the structure of Lie braid groups, their actions, and constructs homomorphisms to symplectomorphism groups of configuration spaces and coadjoint orbits, revealing new connections in geometric group theory.

Contribution

It introduces homomorphisms from Lie braid groups to symplectomorphism groups of configuration spaces and coadjoint orbits, expanding understanding of their topological and geometric properties.

Findings

Constructed homomorphisms to symplectomorphism groups

Linked Lie braid groups with geometric actions

Enhanced understanding of topologies on Lie braid groups

Abstract

We discuss groups corresponding to Kohno Lie algebra of infinitesimal braids and actions of such groups. We construct homomorphisms of Lie braid groups to the group of symplectomorphisms of the space of point configurations in $R^3$ and to groups of symplectomorphisms of coadjoint orbits of SU(n).