Seminar Géométrie et topologie/Geometry-Topology -- A construction of slice knots via annulus modification

11/06/2015 - 11:00
11/06/2015 - 12:00
Jung Hwan Park (Rice University)
PK-5115, Pavillon Président-Kennedy, UQAM

We define an operation on homology four ball which 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, then has been used by Abe and Tange to construct smoothly slice knots. Furthermore we consider n-twist annulus modifications in more general setting to show that any exotically slice knot can be obtained by the image of the unknot in the boundary of a smooth 4-manifold homeomorphic to B4 after an annulus modification.

Last edited by on Mon, 11/02/2015 - 17:13