Noncommutative geometry of algebraic curves

Mathematics – Algebraic Geometry

Scientific paper

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10 pages, final version; to appear Proc. Amer. Math. Soc

Scientific paper

10.1090/S0002-9939-09-09917-1

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 Teichmueller 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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