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Topology and Dynamics: Rokhlin Memorial
August 19-25, 1999
Steklov Institute of Mathematics at St. Petersburg
St. Petersburg, Russia

Organizers
N. Netsvetaev, A. Vershik, O. Viro

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Homological Properties of Virtual Braids
by
Vladimir Vershinin
Sobolev Institute of Mathematics, Novosibirsk 630090, Russia

Virtual knots arise in the study of Gauss diagrams and Vassiliev invariants of usual knots. The group of virtual braids on n strings VBn and its Burau representation to GLnZ[t, t-1] also can be considered. The homological properties of the series of groups VBn and its Burau representation are studied. The following splitting of infinite loop spaces is proved for the plus-construction of the classifying space of the virtual braid group on the infinite number of strings:
Z×BVB¥+ @ W¥ S¥×S1×Y,
where Y is an infinite loop space. Connections with K*Z are discussed.

Date received: June 14, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacy-40.