Inca Foams

TL;DR

This paper investigates a special class of embedded two-foams derived from ribbon torus knots, introducing diagrammatic formalisms and identifying invariants like prime decomposition.

Contribution

It presents new diagrammatic formalisms and invariants for a class of embedded two-foams from ribbon torus knots, including a prime decomposition uniqueness result.

Findings

Multiple equivalent diagrammatic formalisms established.

Identification of key invariants for the two-foams.

Proof of unique prime decomposition for these objects.

Abstract

We study a certain class of embedded two-foams that arise from gluing discs into ribbon torus knots along nonintersecting torus meridians. We exhibit several equivalent diagrammatic formalisms for these objects and identify several of their invariants, including a unique prime decomposition.