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The Alexander polynomial of some virtual knots via the multi-variable Alexander polynomial of links
by
Robert Todd
Mount Mercy University
Coauthors: Micah Chrisman
Almost classical virtual knots are those that are homologically trivial in the thickened Carter surface. Boden et al. show these virtual knots have an Alexander polynomial whose definition is analogous to that for classical knots. Using the theory of virtual covers we show that for some almost classical virtual knots their Alexander polynomial can be found as an evaluation of the classical multi-variable Alexander polynomial of a corresponding two component link. We also comment on an interpretation of the index of a crossing in a virtual knot. Several specific examples will be illustrated.
Date received: September 9, 2016
Copyright © 2016 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 # cbnq-03.