On braided, banded surfaces and ribbon obstructions

TL;DR

This paper explores the use of braid conjugacy class invariants derived from Khovanov-Lee theory to obstruct ribbonness in slice knots, building on Rudolph's work, but finds limitations in effectiveness.

Contribution

It applies Rudolph's methods to braid invariants from Khovanov-Lee theory and analyzes their effectiveness as ribbon obstructions.

Findings

Khovanov-Lee invariants do not provide effective ribbon obstructions

The approach extends Rudolph's work to new classes of braid invariants

Identifies limitations in current invariants for detecting ribbon knots

Abstract

We discuss how to apply work of L. Rudolph to braid conjugacy class invariants to obtain potentially effective obstructions to a slice knot being ribbon. We then apply these ideas to a family of braid conjugacy class invariants coming from Khovanov-Lee theory and explain why we do not obtain effective ribbon obstructions in this case.