Noncommutative geometry of algebraic curves

Nikolaev, Igor

doi:10.1090/S0002-9939-09-09917-1

Noncommutative geometry of algebraic curves
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by Igor V. Nikolaev PDF

Proc. Amer. Math. Soc. 137 (2009), 3283-3290 Request permission

Abstract:

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 Teichmüller space of a curve by the measured foliations due to Douady, Hubbard, Masur and Thurston. The functor maps isomorphic algebraic curves to the stably isomorphic $AF$-algebras.

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