  This paper studies cobordism and concordance for virtual knots. We define the
affine index polynomial, prove that it is a concordance invariant for knots and
links (explaining when it is defined for links), show that it is also invariant
under certain forms of labeled cobordism and study a number of examples in
relation to these phenomena. Information on determinations of the four-ball
genus of some virtual knots is obtained by via the affine index polynomial in
conjunction with results on the genus of positive virtual knots using joint
work with Dye and Kaestner.
