| In this paper, given a knot K, for any integer m we construct a new surface SigmaK( m) from a smoothly embedded surface Sigma in a smooth 4-manifold X by performing a surgery on Sigma. This surgery is based on a modification of the 'rim surgery' which was introduced by Fintushel and Stern, by doing additional twist spinning. We investigate the diffeomorphism type and the homeomorphism type of (X, Sigma) after the surgery. One of the main results is that for certain pairs (X, Sigma), the smooth type of SigmaK(m) can be easily distinguished by the Alexander polynomial of a knot K and the homeomorphism type depends on the number of twist and the knot. In particular, we get new examples of knotted surfaces in CP 2, not isotopic to complex curves, but which are topologically unknotted. |
