Math Colloquium

Speaker: VLADIMIR VERSHININ (Universite de Montpellier, France)

Title: BRAIDS AND HOMOTOPY GROUPS OF SPHERES

Abstract:

We start with the geometrical (naive) definition of braids and then identify them with the fundamental group of configuration space of a manifold. The case of a surface is particular interesting. We recall some classical properties of braids and then pass to Brunnian braids. A braid is Brunnian if it becomes trivial after removing any one of its strands. We describe algebraically the group of Brunnian braids on a general surface, if the surface is not a sphere or projective plane.
In these exceptional cases the group of Brunnian braids is described by an algebraic procedure together with the homotopy groups of a 2-sphere. If there will be time we shall speak about the graded Lie algebra of the descending central series related to Brunnian braid group. It is proved that this is a free Lie algebra and the set of free generators is described.

Bio: 

Vladimir Vershinin is a professor of mathematics at the Alexader Grothendieck Institute in Montpellier, France, and a researcher at the Sobolev Institute of Mathematics, Novosibirsk, Russia.

His interests in Mathematics include Algebraic Topology, and braid groups and their generalizations.

He had hold one year visiting position in Autonoma University of Barcelona, half year positions in the IHES, Paris, and the Poncelet Laboratory, Moscow.