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arXiv:math/9904089 [math.GT]AbstractReferencesReviewsResources

On Homology of Virtual Braids and Burau Representation

V. V. Vershinin

Published 1999-04-18Version 1

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.

Comments: 17 pages, AMSTeX, 17 figures
Journal: J. Knot Theory Ramifications 10 (2001), no. 5, 795-812
Categories: math.GT, math.AT
Subjects: 20J05, 20F36, 20F38, 18D10, 55P35
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