On the cyclic Formality conjecture

Details On the cyclic Formality conjecture On the cyclic Formality conjecture

1999-03-30

arxiv.org/abs/math/9903183v3

Mathematics

Quantum Algebra

24 pages, 5 ps figures

Scientific paper

We conjecture an explicit formula for a cyclic analog of the Formality $L_{\infty}$-morphism [K]. We prove that its first Taylor component, the cyclic Hochschild-Kostant-Rosenberg map, is in fact a morphism (and a quasiisomorphism) of the complexes. To prove it we construct a cohomological version of the Connes-Tsygan bicomplex in cyclic homology. As an application of the cyclic Formality conjecture, we obtain an explicit formula for cyclically invariant deformation quantization.We show that (a more precise version of) the Connes-Flato-Sternheimer conjecture [CFS] on the existence of closed star-products on a symplectic manifold also follows from our conjecture.

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