Noncommutative geometry of algebraic curves

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 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.

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

References in corpus (3)

• Categories of holomorphic vector bundles on noncommutative two-tori
• Real Multiplication and noncommutative geometry
• Non-commutative compactifications and elliptic curves

Cited by in corpus (5)

• Notes on noncommutative geometry
• Mapping class groups are linear
• Elliptic curves and continued fractions
• Trace cohomology revisited
• Toric AF-algebras and faithful representation of the mapping class groups