Equivariant operads , string topology , and Tate cohomology

  title={Equivariant operads , string topology , and Tate cohomology},
  author={Mathematische Annalen},
  • Mathematische Annalen
  • Published 2007
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. Mathematics Subject Classification (2000) 55N91 · 55P43 · 55P92 · 55R12 · 14D22 · 18D50