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  On deformation quantization of quadratic Poisson structuresMerkoulov (merkulov), Serguei  ; E-print/Working paper (2021) We study the deformation complex of the dg wheeled properad of Z-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application ... [more ▼] We study the deformation complex of the dg wheeled properad of Z-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application we show that the Grothendieck-Teichmüller group acts on the genus completion of that wheeled properad faithfully and essentially transitively. As a second application we classify all universal quantizations of Z-graded quadratic Poisson structures together with the underlying (so called) homogeneous formality maps. [less ▲] Detailed reference viewed: 82 (0 UL) Differentials on graph complexes II: hairy graphs; ; Zivkovic, Marko in Letters in Mathematical Physics (2017), 107(10), 17811797 We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spectral sequences converging ... [more ▼] We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spectral sequences converging to zero whose first pages contain the hairy graph cohomology. Our results yield a way to construct many nonzero hairy graph cohomology classes out of (known) non-hairy classes by studying the cancellations in those sequences. This provide a first glimpse at the tentative global structure of the hairy graph cohomology. [less ▲] Detailed reference viewed: 134 (5 UL)On quantizable odd Lie bialgebras; Merkulov, Sergei ; in Letters in Mathematical Physics (2016), 106(9), 1199-1215 The notion of a quantizable odd Lie bialgebra is introduced. A minimal resolution of the properad governing such Lie bialgebras is constructed. Detailed reference viewed: 188 (5 UL)Quillen homology for operads via Gröbner basesDotsenko, Vladimir ; in Documenta Mathematica (2013), 18 Detailed reference viewed: 39 (1 UL) |
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