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Upper bounds on Virtual Bridge Numbers
by
Puttipong Pongtanapaisan
University of Iowa
The virtual bridge number of a knot is the smallest number of overbridges taken over all virtual knot diagrams of the knot. A naive upper bound obtained from counting the number of overbridges of a virtual knot diagram representing the knot can be much larger than the actual virtual bridge number. In this talk, I will define the Wirtinger number of a knot, which is the minimum number of generators of the knot group over all meridional presentations in which every relation is an iterated Wirtinger relation. The Wirtinger number turns out to be equal to the virtual bridge number, and we will see that the Wirtinger number of a diagram representing the knot gives a stronger upper bound on the virtual bridge number of the knot.
Date received: April 4, 2018
Copyright © 2018 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 # cboy-15.