14 citations · 34 across the 5 of their papers we have counts for
16 papers
An explicit formula for the deformation quantization of Lie bialgebras
Boris Shoikhet
A model of 3-dimensional topological quantum field theory is rigorously constructed. The results are applied to an explicit formula for deformation quantization of any finite-dimen…
Riemann-Roch-Hirzebruch theorem and Topological Quantum Mechanics
Boris Feigin, Andrey Losev, Boris Shoikhet
In the present paper we discuss an independent on the Grothendieck-Sato isomorphism approach to the Riemann-Roch-Hirzebruch formula for an arbitrary differential operator. Instead…
A concept of PROP and deformation theory of (co)associative bialgebras
Boris Shoikhet
We introduce a concept of PROP generalizing the Kontsevich concept of PROP. We prove that some Stasheff-type compactification of the Kontsevich spaces de…
An explicit deformation theory of (co)associative bialgebras
Boris Shoikhet
The paper has been withdrawn.
The CROCs, non-commutative deformations, and (co)associative bialgebras
Boris Shoikhet
We compactify the spaces introduced by Maxim Kontsevich. The initial idea was to construct an algebra governing the deformations of a (co)associative bialgebra.…
Tsygan formality and Duflo formula
Boris Shoikhet
We prove the 0-(co)homology part of the conjecture on the cup-products on tangent cohomology in the Tsygan formality [Sh2]. We discuss its applications to the Duflo formula.