Band Number and the Double Slice Genus

2019/01/22 by McDonald, Clayton · 1 citation
#57M27 (Primary) 57M25 #57Q45 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1901.07625

Abstract

We study the double slice genus of a knot, a natural generalization of slice genus. We define a notion called band number, a natural generalization of band unknotting number, and prove it is an upper bound on double slice genus. Our bound is based on an analysis of broken surface diagrams and embedding properties of 3-manifolds in 4-manifolds.

Cited by

• Integer inequalities between knot invariants, skein tree depth and delta-crossing numbers

Related

• A lower bound for the double slice genus
• Slice genus, T-genus and 4-dimensional clasp number
• A lower bound for the doubly slice genus from signatures
• On slicing invariants of knots
• On the slice genus of generalized algebraic knots