We give a new construction of slice knots via annulus twists. The simplest slice knots obtained by our method are those constructed by Omae. In this paper, we introduce a sufficient condition for given slice knots to be ribbon, and prove that all Omae's knots are ribbon.
We will give an explicit formula of Ozsváth-Szabó's correction terms of lens spaces. Applying the formula to a restriction studied by P. Ozsváth and Z. Szabó in [12] and [13], we obtain several constraints of lens spaces which are constructed by a positive Dehn surgery in 3-sphere. Some of the constraints are results which are analogous to results which were known in [6] and [20] before. The constraints completely determine knots yielding L( p, 1) by positive Dehn surgery.
We consider the problem when lens spaces are given from homology spheres, and demonstrate that many lens spaces are obtained from L-space homology sphere which the correction term d(Y ) is equal to 2. We show an inequality of slope and genus when Y is L-space and Y p (K) is lens space.
We show that for any positive integer m, there exist order n Stein corks (Cn,m, τ C n,m ). The boundaries are cyclic branched covers of slice knots embedded in the boundary of a cork. By applying these corks to generalized forms, we give a method producing examples of many finite order corks, which are possibly not Stein cork. The examples of the Stein corks give n homotopic and contactomorphic but non-isotopic Stein filling contact structures for any n.
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