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• W2103407172 abstract "First we argue that many BV and homotopy BV structures, including both familiar and new examples, arise from a common underlying construction. The input of this construction is a cyclic operad along with a cyclically invariant Maurer-Cartan element in an associated Lie algebra. Using this result we introduce and study the operad of cyclically invariant operations, with instances arising in cyclic cohomology and $S^1$ equivariant homology. We compute the homology of the cyclically invariant operations; the result being the homology operad of $mathcal{M}_{0,n+1}$, the uncompactified moduli spaces of punctured Riemann spheres, which we call the gravity operad after Getzler. Motivated by the line of inquiry of Deligne's conjecture we construct `cyclic brace operations' inducing the gravity relations up-to-homotopy on the cochain level. Motivated by string topology, we show such a gravity-BV pair is related by a long exact sequence. Examples and implications are discussed in course." @default.
• W2103407172 created "2016-06-24" @default.
• W2103407172 creator A5069732750 @default.
• W2103407172 date "2014-09-19" @default.
• W2103407172 modified "2023-09-27" @default.
• W2103407172 title "Maurer-Cartan Elements and Cyclic Operads" @default.
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• W2103407172 hasPublicationYear "2014" @default.
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