Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex

TL;DR

This paper introduces a new annular concordance invariant derived from a combinatorial link Floer complex, providing bounds on band rank and refining transverse invariants, with implications for braid and transverse link properties.

Contribution

It defines a novel annular concordance invariant, reformulates it via a modified chain complex, and refines the transverse invariant hat, connecting it to braid and transverse link properties.

Findings

The invariant provides bounds on band rank for braids.

A modified chain complex offers a new formulation of the invariant.

Refinement of the transverse invariant hat enhances understanding of transverse links.

Abstract

We define an annular concordance invariant and study its properties. When specialized to braids, this invariant gives bounds on band rank. We introduce a modified chain complex to reformulate the invariant. Then, by focusing on a special case, we give a refinement of the transverse invariant $\hat{\theta}$. We also study the relationship of this invariant with transverse and braid monodromy properties.