Virtual singular braids and links
Carmen Caprau, Andrew de la Pena, and Sarah McGahan
TL;DR
This paper introduces virtual singular braids, defines their algebraic structure, and establishes foundational theorems linking braids to links, expanding the mathematical framework for virtual and singular knot theory.
Contribution
It defines the virtual singular braid monoid, provides multiple presentations, and proves Alexander- and Markov-type theorems for virtual singular links.
Findings
Defined the virtual singular braid monoid with generators and relations
Proved Alexander- and Markov-type theorems for virtual singular links
Presented an alternative, simplified presentation of the braid monoid
Abstract
Virtual singular braids are generalizations of singular braids and virtual braids. We define the virtual singular braid monoid via generators and relations, and prove Alexander- and Markov-type theorems for virtual singular links. We also show that the virtual singular braid monoid has another presentation with fewer generators.
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