Geodesic
Higher cyclic operads
Hackney, Philip1 ; Robertson, Marcy2 ; Yau, Donald3
1 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
2 School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria, Australia
3 Department of Mathematics, The Ohio State University at Newark, Newark, OH, United States
Algebraic and Geometric Topology, Tome 19 (2019) no. 2, pp. 863-940

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2019.19.863
Classification : 05C05, 18D50, 55P48, 55U35, 37E25, 55U10, 18G30, 18G55
Keywords: cyclic operad, dendroidal set, Quillen model category, Reedy category

Hackney, Philip 1 ; Robertson, Marcy 2 ; Yau, Donald 3

1 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
2 School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria, Australia
3 Department of Mathematics, The Ohio State University at Newark, Newark, OH, United States 
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Hackney, Philip; Robertson, Marcy; Yau, Donald. Higher cyclic operads. Algebraic and Geometric Topology, Tome 19 (2019) no. 2, pp. 863-940. doi: 10.2140/agt.2019.19.863

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