Rectangular diagrams of foliations

TL;DR

The paper introduces rectangular diagrams for foliations in the three-sphere and demonstrates that any co-orientable finite depth foliation outside a link can be represented by such diagrams, compatible with the link's diagram.

Contribution

It presents a new diagrammatic method for representing foliations in three-spheres, linking foliation structures with link diagrams.

Findings

Any co-orientable finite depth foliation outside a link admits a compatible rectangular diagram.

Rectangular diagrams can effectively represent foliation structures in the three-sphere.

The method provides a new tool for studying foliations in knot theory contexts.

Abstract

A concept of a rectangular diagram of a foliation in the three-sphere is introduced. It is shown that any co-orientable finite depth foliation in the complement of a link admits a presentation by a rectangular diagram compatible with the given rectangular diagram of the link.