A lower bound for the double slice genus

Wenzhao Chen

Published 2018-01-12Version 1

In this paper, we develop a lower bound for the double slice genus of a knot in the 3-sphere using Casson-Gordon invariants. As an application, we show that the difference between the slice genus and the double slice genus can be arbitrarily large. As an analogue to the double slice genus, we also define the superslice genus of a knot, and give both an upper bound and a lower bound. In particular, through the study of superslice genus we show that the degree of the Alexander polynomial is an upper bound for the topological double slice genus of a ribbon knot.