Operadic actions on long knots and 2–string links

Batelier, Etienne; Ducoulombier, Julien

doi:10.2140/agt.2023.23.833

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Operadic actions on long knots and $2$–string links

Etienne Batelier and Julien Ducoulombier

Algebraic & Geometric Topology 23 (2023) 833–882

DOI: 10.2140/agt.2023.23.833

Abstract

We realize the space of $2$ –string links $ℒ$ as a free algebra over a colored operad denoted by $𝒮 𝒞 ℒ$ (for “Swiss-cheese for links”). This result extends works of Burke and Koytcheff about the quotient of $ℒ$ by its center, and is compatible with Budney’s freeness theorem for long knots. From an algebraic point of view, our main result refines Blaire, Burke and Koytcheff’s theorem on the monoid of isotopy classes of string links. Topologically, it expresses the homotopy type of the isotopy class of a $2$ –string link in terms of the homotopy types of the classes of its prime factors.

Keywords

space of knots, space of links, little cubes operad, Swiss-cheese operad, embedding, homotopy theory

Mathematical Subject Classification

Primary: 57R40

Secondary: 55P48, 55U40, 57M99

References

Publication

Received: 2 March 2021

Revised: 22 October 2021

Accepted: 10 November 2021

Published: 9 May 2023

Authors

Etienne Batelier
Mathematisches Institut Universität Münster Münster Germany

Julien Ducoulombier
Université Sorbonne Paris Nord Villetaneuse France

Open Access made possible by participating institutions via Subscribe to Open.

Volume 23, issue 2 (2023)