On Homology of Virtual Braids and Burau Representation
V. V. Vershinin
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 VBn 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(S0), S1 and an infinite loop space Y. Connections with the K-functor of the integers are discussed.
Create a lesson
Related papers
Smooth and Topological Nonorientable Four-Genera of Low-Crossing Knots
Seong-Jin Lee
Universal bounds for decompositions of PL manifolds
Rustam Sadykov
A surface-group action on real-hyperbolic space with no Cannon--Thurston map
Bruno Dular
Combination Theorems and the Farrell--Jones Conjecture for Graph Products of Pairs
I. Gkeneralis, S. Prassidis
Multivariable Alexander polynomials of twisted torus links via Dehn surgery
Birch Bryant
Quasimorphisms and bounded cohomology of transformation groups of nonorientable surfaces
Michael Brandenbursky