Unoriented band surgery on knots and links
  We consider a relation between two kinds of unknotting numbers defined by using a band surgery on unoriented knots; the band-unknotting number and H(2)-unknotting number, which we may characterize in terms of the first Betti number of surfaces in S^3 spanning the knot and the trivial knot. We also give several examples for these numbers. 
Tetsuya Abe and Taizo Kanenobu
math.GT