In this paper we show that, after completing in the $I$-adic topology, Turaev cobracket on vector space freely generated by closed geodesics a smooth, complex algebraic curve $X$ with quasi-algebraic framing is morphism of mixed Hodge structure. We combine results previous Goldman bracket to construct torsors solutions Kashiwara–Vergne problem all genera. The so constructed form torsor under pr...

The classification of surfaces theorem was one of the earliest triumphs of algebraic topology. It states that any closed connected surface is homeomorphic to the sphere, the connected sum of n tori, or the connected sum of m projective planes. This paper begins by defining the geometric, topological, and algebraic tools necessary to understanding the theorem, then proceeds through the technical...

It appears that if dimcZ = a. dim X > 2, one may consider X as an algebraic variety too but in some new sense. One can generalize the conception of the abstract variety of A. Weil by substituting the etale topology of Grothendieck for the topology of Zariski. One gets the objects which M. Artin called "etale schemes" and the author called "minischemes". Later, M. Artin introduced the term "alge...

We propose the representability hierarchy of algebraic functions over C, which relates classic questions like the unsolvability of the quintic by radicals to unresolved questions like Hilbert’s 13th problem in its original algebraic form. We construct the theory of algebraic functions via both superpositions and algebraic geometry and then justify the known positions of the universal algebraic ...

Graph transformation systems have been introduced for the formal specification of software systems. States are thereby modeled as graphs, and computations as graph derivations according to the rules of the specification. Operations on graph derivations provide means to reason about the distribution and composition of computations. In this paper we discuss the development of an algebra of graph ...