SLICING KNOTS IN DEFINITE 4-MANIFOLDS

We study the CP2-slicing number of knots, i.e. the smallest m >= 0 such that a knot K subset of S3 bounds a properly embedded, null-homologous disk in a punctured connected sum (#mCP2)x. We find knots for which the smooth and topological CP2-slicing numbers are both finite, nonzero, and distinct. To do this, we give a lower bound on the smooth CP2-slicing number of a knot in terms of its double branched cover and an upper bound on the topological CP2-slicing number in terms of the Seifert form.