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math.GT2009
Lower bounds on virtual crossing number and minimal surface genus
Kumud Bhandari, H. A. Dye, Louis H. Kauffman
We compute lower bounds on the virtual crossing number and minimal surface genus of virtual knot diagrams from the arrow polynomial. In particular, we focus on several interesting…
math.GT2008
Virtual Crossing Number and the Arrow Polynomial
H. A. Dye, Louis H. Kauffman
We introduce a new polynomial invariant of virtual knots and links and use this invariant to compute a lower bound on the virtual crossing number and the minimal surface genus.
math.GT2006
Virtual Homotopy
H. A. Dye, Louis H. Kauffman
Two welded (respectively virtual) link diagrams are homotopic if one may be transformed into the other by a sequence of extended Reidemeister moves, classical Reidemeister moves, a…