On Homology of Virtual Braids and Burau Representation
Geometric Topology
2012-02-22 v1 Algebraic Topology
Abstract
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.
Keywords
Cite
@article{arxiv.math/9904089,
title = {On Homology of Virtual Braids and Burau Representation},
author = {V. V. Vershinin},
journal= {arXiv preprint arXiv:math/9904089},
year = {2012}
}
Comments
17 pages, AMSTeX, 17 figures