Equivariant operads, string topology, and Tate cohomology
arXiv:math/0605080
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.
36 pages, 1 figure. Changes: main proofs and exposition streamlined, new section on continuous cohomology of operads, font changed. To appear in Math. Ann