Volume 19, issue 2 (2019)

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

Volume 19
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

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

Author Index
The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
 
Other MSP Journals
Higher cyclic operads

Philip Hackney, Marcy Robertson and Donald Yau

Algebraic & Geometric Topology 19 (2019) 863–940
Abstract

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.

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