A lower bound for the double slice genus

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.

18 pages, 6 figures, to appear in Trans. Amer. Math. Soc

References in corpus (4)

• The degree of the Alexander polynomial is an upper bound for the topological slice genus
• Distinguishing topologically and smoothly doubly slice knots
• Doubly slice knots with low crossing number
• On smoothly superslice knots

Cited by in corpus (1)

• Balanced algebraic unknotting, linking forms, and surfaces in three- and four-space