Genuine equivariant operads

Luis A. Pereira; Peter Bonventre

Genuine equivariant operads

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arxiv 1707.02226 v3 pith:VPJQLSTZ submitted 2017-07-07 math.AT

Peter Bonventre , Luis A. Pereira This is my paper · ORCID

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keywords operadsequivariantgenuinebuildmodelstructurealgebraicapplication

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abstract

We build new algebraic structures, which we call genuine equivariant operads, which can be thought of as a hybrid between equivariant operads and coefficient systems. We then prove an Elmendorf-Piacenza type theorem stating that equivariant operads, with their graph model structure, are equivalent to genuine equivariant operads, with their projective model structure. As an application, we build explicit models for the $N_{\infty}$-operads of Blumberg and Hill.

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Homotopy theory of equivariant operads with fixed colors
math.AT 2019-08 accept novelty 7.0 of 10

Fixed-color equivariant simplicial operads admit model structures whose weak equivalences are detected by graph subgroups or by any chosen (G,Sigma)-family of subgroups.

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