Volume 19, issue 2 (2019)

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

Volume 24, 1 issue

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
Higher cyclic operads

Philip Hackney, Marcy Robertson and Donald Yau

Algebraic & Geometric Topology 19 (2019) 863–940

We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specifically, we introduce a category Ξ of trees, which carries a tight relationship to the Moerdijk–Weiss category of rooted trees Ω. We prove a nerve theorem exhibiting colored cyclic operads as presheaves on Ξ which satisfy a Segal condition. Finally, we produce a Quillen model category whose fibrant objects satisfy a weak Segal condition, and we consider these objects as an up-to-homotopy generalization of the concept of cyclic operad.

cyclic operad, dendroidal set, Quillen model category, Reedy category
Mathematical Subject Classification 2010
Primary: 05C05, 18D50, 55P48, 55U35
Secondary: 37E25, 55U10, 18G30, 18G55
Received: 10 October 2017
Revised: 9 June 2018
Accepted: 2 August 2018
Published: 12 March 2019
Philip Hackney
Institut für Mathematik
Universität Osnabrück
Max-Planck-Institut für Mathematik
Department of Mathematics
University of Louisiana at Lafayette
Lafayette, LA
United States
Marcy Robertson
School of Mathematics and Statistics
University of Melbourne
Donald Yau
Department of Mathematics
The Ohio State University at Newark
Newark, OH
United States