# Moscow Mathematical Journal

Volume 12, Issue 4, October–December 2012 pp. 803–824.

On Topologies on Malcev Completions of Braid Groups**Authors**: Yury Neretin

**Author institution:**Math. Dept., University of Vienna, Nordbergstrasse, 15, Vienna, Austria,

Institute for Theoretical and Experimental Physics, Bolshaya Cheremushkinskaya, 25, Moscow 117259, Russia,

Mech. Math. Dept., Moscow State University, Vorob'evy Gory, Moscow

**Summary:**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 $\mathbb{R}^{3}$ and to groups of symplectomorphisms of coadjoint orbits of $\mathrm{SU}(n)$.

2010 Mathematics Subject Classification. 20F36, 20F18, 17B65, 22E65, 58F05

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