Volume 15, issue 6 (2015)

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

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
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
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
A colored operad for string link infection

John Burke and Robin Koytcheff

Algebraic & Geometric Topology 15 (2015) 3371–3408
Abstract

Budney constructed an operad that encodes splicing of knots and further showed that the space of (long) knots is generated over this splicing operad by the space of torus knots and hyperbolic knots. This generalized the satellite decomposition of knots from isotopy classes to the level of the space of knots. Infection by string links is a generalization of splicing from knots to links. We construct a colored operad that encodes string link infection. We prove that a certain subspace of the space of 2–component string links is generated over a suboperad of our operad by its subspace of prime links. This generalizes a result from joint work with Blair from isotopy classes of string links to the space of string links. Furthermore, all the relations in the monoid of 2–string links (as determined in our joint work with Blair) are captured by our infection operad.

Keywords
string links, infection, operads, spaces of links, spaces of knots
Mathematical Subject Classification 2010
Primary: 57M25, 18D50, 55P48, 57R40, 57R52
References
Publication
Received: 11 August 2014
Revised: 25 February 2015
Accepted: 28 February 2015
Published: 12 January 2016
Authors
John Burke
Department of Mathematics
Rhode Island College
Providence, RI 02908-1991
USA
Robin Koytcheff
Department of Mathematics and Statistics
University of Massachusetts
Amherst, MA 01003
USA
http://people.math.umass.edu/~koytcheff