Sergei Chmutov

Learn More
We generalize the natural duality of graphs embedded into a surface to a duality with respect to a subset of edges. The dual graph might be embedded into a different surface. We prove a relation between the signed Bollobás-Riordan polynomials of dual graphs. This relation unifies various recent results expressing the Jones polynomial of links as(More)
We introduce and study the structure of an algebra in the linear space spanned by all regular 3-valent graphs with a prescribed order of edges at every vertex, modulo certain relations. The role of this object in various areas of low dimensional topology is discussed. 0 Introduction Regular graphs of degree 3, i. e. graphs in which every vertex is incident(More)
We review the explicit formulas for Arnold's generic curve invari-ants due to Viro, Shumakovich and Polyak and add some remarks concerning the invariants of spherical curves and curves immersed into arbitrary orientable surfaces. A generic curve is a smooth immersion of the circle into the plane whose only singularities are transversal double points. Up to(More)
There are several fascinating relations of plane immersed curves and links. One of them which goes through Legendrian links led Arnold [5] to discovery of three simple invariants J, J−, St of such a curve. N. A’Campo in [2] suggested another construction of a link from a generic immersion of a curve into a 2-disk. It is tightly related to the singularity(More)