Sergey A. Merkulov

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Contrary to the classical methods of quantum mechanics, the deformation quan-tization can be carried out on phase spaces which are not even topological manifolds. In particular, the Moyal star product gives rise to a canonical functor F from the category of affine analytic spaces to the category of associative (in general, non-commutative) C-algebras.(More)
" The genetic code appears to be universal;. .. " Britannica. 0. Abstract. The first instances of algebraic and topological strongly homotopy, or infinity, structures have been discovered by Stasheff [St] long ago. Since that time infinities have acquired a prominent role in algebraic topology and homological algebra. We argue in this paper that some(More)
This is a comment on the Kuranishi method of constructing analytic deformation spaces. It is based on a simple observation that the Kuranishi map can always be inverted in the category of L ∞-algebras. The L ∞-structure obtained by this inversion is used to define an " unobstructed " deformation functor which is always representable by a smooth pointed(More)
The first instances of graph complexes have been introduced in the theory of operads and props which have found recently lots of applications in algebra, topology and geometry. Another set of examples has been introduced by Kontsevich [Ko1] as a way to expose highly non-trivial interrelations between certain infinite dimensional Lie algebras and topological(More)
The squalene synthase (SQS) gene encodes a key regulatory enzyme, farnesyl-diphosphate farnesyltransferase (EC 2.5.1.21), in sterol biosynthesis. The SQS1 gene was isolated from a subgenomic library of the industrially important yeast Yarrowia lipolytica, using PCR-generated probes. Probes were based on conserved regions of homologues from different(More)
It is shown that any compact Kähler manifold M gives canonically rise to two strong homotopy algebras, the first one being associated with the Hodge theory of the de Rham complex and the second one with the Hodge theory of the Dolbeault complex. In these algebras the product of two harmonic differential forms is again harmonic. If M happens to be a(More)
0. Introduction. Let M be a simply connected closed oriented n-dimensional manifold, and LM := Map C ∞ (S 1 , M) the associated free loop space. String topology of Chas and Sul-livan [CS] deals with an ample family of algebraic operations on the ordinary and equivariant homologies of LM , the most important being a graded commutative associative product,
0.1. Little disks operad and Hertling-Manin's F-manifolds. Frobenius manifolds created by Dubrovin in 1991 from rich theoretical physics material have been found since in many different fragments of mathematics — quantum cohomology and mirror symmetry, complex geometry , symplectic geometry, singularity theory, integrable systems — raising hopes for(More)