A construction of slice knots via annulus modifications

Abstract

We define an operation on a homology B-4 that we call an n-twist annulus modification. We give a new construction of smoothly slice knots and exotically slice knots via n-twist annulus modifications. As an application, we present a new example of a smoothly slice knot with non-slice derivatives. Such examples were first discovered by Cochran and Davis. Also, we relate n-twist annulus modifications to n-fold annulus twists which was first introduced by Osoinach and has been used by Abe and Tange to construct smoothly slice knots. Furthermore we show that any exotic slice disk can be obtained by an annulus modification performed on some exotic slice disk bounding the unknot. (C) 2018 Elsevier B.V. All rights reserved.