Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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

We realize the space of 2–string links as a free algebra over a colored operad denoted by 𝒮𝒞 (for “Swiss-cheese for links”). This result extends works of Burke and Koytcheff about the quotient of 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.

space of knots, space of links, little cubes operad, Swiss-cheese operad, embedding, homotopy theory
Mathematical Subject Classification
Primary: 57R40
Secondary: 55P48, 55U40, 57M99
Received: 2 March 2021
Revised: 22 October 2021
Accepted: 10 November 2021
Published: 9 May 2023
Etienne Batelier
Mathematisches Institut
Universität Münster
Julien Ducoulombier
Université Sorbonne Paris Nord

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