20 citations · 102 across the 71 of their papers we have counts for
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On complex and noncommutative tori
Igor Nikolaev
The "noncommutative geometry" of complex algebraic curves is studied. As first step, we clarify a morphism between elliptic curves, or complex tori, and C*-algebras T_t={u,v | vu=e…
Geodesic laminations revisited
Igor Nikolaev
The Bratteli diagram is an infinite graph which reflects the structure of projections in a C*-algebra. We prove that every strictly ergodic unimodular Bratteli diagram of rank 2g+m…
Thurston's norm revisited
Igor Nikolaev
We study the Thurston norm on the second homology of a 3-manifold M, which is the surface bundle over the circle with a pseudo-Anosov monodromy. A novelty of our approach consists…
Arithmetic of hyperbolic 3-manifolds
Igor Nikolaev
This note is an elaboration of the ideas and intuitions of Grothendieck and Weil concerning the "arithmetic topology". Given 3-dimensional manifold M fibering over the circle we in…