A colored operad for string link infection

Burke, John; Koytcheff, Robin

doi:10.2140/agt.2015.15.3371

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A colored operad for string link infection

John Burke and Robin Koytcheff

Algebraic & Geometric Topology 15 (2015) 3371–3408

DOI: 10.2140/agt.2015.15.3371

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

Volume 15, issue 6 (2015)