Studying links via booklinks: A Markov theorem

TL;DR

This paper introduces 'book links' as a new generalization of braids within open book decompositions and proves a Markov theorem for this broader class, extending open book foliation theory.

Contribution

It presents a novel class of links called 'book links' and establishes a Markov theorem for them, expanding the understanding of link representations in open book decompositions.

Findings

'Book links' include braids and plats as special cases

A Markov theorem is proved for 'book links'

Extension of open book foliation theory to this new setting

Abstract

We introduce "book links" as a generalization of braids in open book decompositions; this new class of objects includes both braids and plats as special cases. We then prove a version of Markov's theorem in this general setting by extending the theory of open book foliations.