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Equivariant operads, string topology, and Tate cohomology

Craig Westerland
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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 C_2 (which is an S^1 operad) we obtain variations on Getzler's gravity operad, which we show governs the Chas-Sullivan string bracket.

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Craig Westerland. 2007-08-01. Equivariant operads, string topology, and Tate cohomology. https://arxiv.org/abs/math/0605080

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