Volume 18, issue 5 (2018)

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Encoding equivariant commutativity via operads

Javier J Gutiérrez and David White

Algebraic & Geometric Topology 18 (2018) 2919–2962
Abstract

We prove a conjecture of Blumberg and Hill regarding the existence of N–operads associated to given sequences = (n)n of families of subgroups of G × Σn. For every such sequence, we construct a model structure on the category of G–operads, and we use these model structures to define E–operads, generalizing the notion of an N–operad, and to prove the Blumberg–Hill conjecture. We then explore questions of admissibility, rectification, and preservation under left Bousfield localization for these E–operads, obtaining some new results as well for N–operads.

Keywords
model category, homotopy category, equivariant homotopy theory, equivariant spectra, operads
Mathematical Subject Classification 2010
Primary: 55P42, 55P48, 55P60, 55P91, 55U35
References
Publication
Received: 7 July 2017
Revised: 28 February 2018
Accepted: 20 March 2018
Published: 22 August 2018
Authors
Javier J Gutiérrez
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Barcelona
Spain
http://www.ub.edu/topologia/gutierrez
David White
Department of Mathematics
Denison University
Granville, OH
United States
http://personal.denison.edu/~whiteda