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New Bounds on Virtual Bridge Number and Virtual Ascending Number
by
Noureen Khan
University of North Texas at Dallas
The virtual bridge number, vb(K) is the minimum number of bridges over all the Gauss diagrams realizing a virtual knot K. We review and analyze the notion to generalize some other virtual knot theory invariants, in particular, the virtual ascending number, av(K). We show that there are infinitely many homotopy classes of virtual knots each of which contains vb(K) = av(K). Some fundamental results and a table of invariants, vb(K) and av(K) for virtual knots with real crossing number less than 5 are given.
Date received: December 1, 2014
Copyright © 2014 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbjz-18.