Abstract:
From an operad C of topological spaces with an action of a group G, we construct new operads in spectra from 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 operads C_k (which are SO(k)-operads) we obtain an operad governing the Chas-Sullivan string bracket and conjecturally higher dimensional versions. If time permits, we will comment on how these constructions fit into Ginzburg-Kapranov's notion of Kozul duality for operads.
