Abstract
From an operad \(\fancyscript {C}\) 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 \(\fancyscript {C}\) is trivial. Applying this theory to the little disk operad \(\fancyscript {C}_2\) (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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Westerland, C. Equivariant operads, string topology, and Tate cohomology. Math. Ann. 340, 97–142 (2008). https://doi.org/10.1007/s00208-007-0140-0
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DOI: https://doi.org/10.1007/s00208-007-0140-0