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Mathematische Annalen

, Volume 340, Issue 1, pp 97–142 | Cite as

Equivariant operads, string topology, and Tate cohomology

  • Craig Westerland
Article

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.

Mathematics Subject Classification (2000)

55N91 55P43 55P92 55R12 14D22 18D50 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of Wisconsin-MadisonMadisonUSA

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