A lower bound for the double slice genus

TL;DR

This paper introduces a new lower bound for the double slice genus of knots using Casson-Gordon invariants, demonstrating it can be arbitrarily larger than twice the slice genus, and also explores the superslice genus with bounds.

Contribution

It provides the first lower bound for the double slice genus via Casson-Gordon invariants and introduces the superslice genus with bounds in the topological category.

Findings

Double slice genus can be arbitrarily larger than twice the slice genus.

Established a lower bound for the double slice genus using Casson-Gordon invariants.

Defined the superslice genus and provided bounds in the topological setting.

Abstract

In this paper, we develop a lower bound for the double slice genus of a knot using Casson-Gordon invariants. As an application, we show that the double slice genus can be arbitrarily larger than twice the slice genus. 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 the topological category.