Equivariant operads, string topology, and Tate cohomology

2006/05/03 by Craig Westerland, Westerland, Craig · 1 citation
Mathematics · #14D22 #18D50 #55N91 #55P43 #55P92 #55R12 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:14D22 #msc:18D50 #msc:55N91 #msc:55P43 #msc:55P92 #msc:55R12

paper · pdf · doi:10.48550/arxiv.math/0605080

36 pages, 1 figure. Changes: main proofs and exposition streamlined, new section on continuous cohomology of operads, font changed. To appear in Math. Ann

openalex publication_date 2006/05/03 · arxiv created 2007/08/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

From an operad C with an action of a group G, we construct new operads using the homotopy fixed point and orbit spectra. These new operads are shown to be equivalent when the generalized G-Tate cohomology of C is trivial. Applying this theory to the little disk operad C₂ (which is an S¹ operad) we obtain variations on Getzler's gravity operad, which we show governs the Chas-Sullivan string bracket.

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• String topology and the based loop space

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