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We consider a relation between two kinds of unknotting numbers defined byusing a band surgery on unoriented knots; the band-unknotting number andH(2)-unknotting number, which we may characterize in terms of the first Bettinumber of surfaces in S^3 spanning the knot and the trivial knot. We also giveseveral examples for these numbers.

Unoriented band surgery on knots and links