Alternating Virtual Knots

Abstract

In this thesis, we study alternating virtual knots. We show the Alexander polynomial of an almost classical alternating knot is alternating. We give a characterization theorem for alternating knots in terms of Goeritz matrices. We prove any reduced alternating diagram has minimal genus, and use this to prove the frst Tait Conjecture for virtual knots, namely any reduced diagram of an alternating virtual knot has minimal crossing number.