Summary
Motivated by the problem of deformation quantization we introduce and study directed graph complexes with oriented loops and wheels – differential graded (dg) wheeled props. We develop a new technique for computing cohomology groups of such graph complexes and apply it to several concrete examples such as the wheeled completion of the operad of strongly homotopy Lie algebras and the wheeled completion of the dg prop of Poisson structures. The results lead to a new notion of a wheeled Poisson structure and to a new theorem on deformation quantization of arbitrary wheeled Poisson manifolds.
2000 Mathematics Subject Classifications: 17B66, 18D50, 53D17, 53D55
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To Yuri Ivanovich Manin on his 70th birthday
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Merkulov, S.A. (2009). Graph Complexes with Loops and Wheels. In: Tschinkel, Y., Zarhin, Y. (eds) Algebra, Arithmetic, and Geometry. Progress in Mathematics, vol 270. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4747-6_10
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DOI: https://doi.org/10.1007/978-0-8176-4747-6_10
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