20 citations · 102 across the 71 of their papers we have counts for
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Toric AF-algebras and faithful representation of the mapping class groups
Igor Nikolaev
There exists a covariant non-injective functor from the space of generic Riemann surfaces to the so-called toric AF-algebras; such a functor maps isomorphic Riemann surfaces to the…
AF-algebras and topology of 3-manifolds
Igor Nikolaev
We construct a functor which maps conjugate pseudo-Anosov automorphisms of a surface to the so-called stably isomorphic stationary AF-algebras; the functor gives new topological in…
Ordered abelian groups over a CW complex
Igor Nikolaev
If X is a CW complex, one can assign to each point of X an ordered abelian group of finite rank whose subset of positive elements depends continuously on the points of X. A locally…
CMC-surfaces, flat structures and umbilical points
Igor Nikolaev
A short proof of the Caratheodory conjecture about index of an isolated umbilic on the convex 2-dimensional sphere is suggested. The argument is based on the study of geodesic line…
On embedding of the Bratteli diagram into a surface
Igor Nikolaev
We study C*-algebras O_λ which arise in dynamics of the interval exchange transformations and measured foliations on compact surfaces. Using Koebe-Morse coding of geodesic lines, w…
Noncommutative geometry of algebraic curves
Igor Nikolaev
A covariant functor from the category of generic complex algebraic curves to a category of the AF-algebras is constructed. The construction is based on a representation of the Teic…