On Homology of Virtual Braids and Burau Representation

Details On Homology of Virtual Braids and Burau Representation On Homology of Virtual Braids and Burau Representation

1999-04-18

arxiv.org/abs/math/9904089v1

J. Knot Theory Ramifications 10 (2001), no. 5, 795-812

Mathematics

Geometric Topology

17 pages, AMSTeX, 17 figures

Scientific paper

Virtual knots arise in the study of Gauss diagrams and Vassiliev invariants of usual knots. Virtual braids correspond naturally to virtual knots. We consider the group of virtual braids on n strings VB_n and its Burau representation, in particular we study their homological properties. We prove that the plus-construction of the classifying space of the virtual braid group on the infinite number of strings is an infinite loop space which is equivalent to a product of Q(S^0), S^1 and an infinite loop space Y. Connections with the K-functor of the integers are discussed.

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