Riemann surfaces and AF-algebras

Details Riemann surfaces and AF-algebras Riemann surfaces and AF-algebras

2007-10-17

arxiv.org/abs/0710.3357v5

Mathematics

Operator Algebras

22 pages, 2 figures; minor changes

Scientific paper

For a generic set in the Teichmueller space, we construct a covariant functor with the range in a category of the AF-algebras. The functor maps isomorphic Riemann surfaces to the stably isomorphic AF-algebras. Our construction is based on a Hodge theory for measured foliations, elaborated by Hubbard, Masur and Thurston. As a special case, one obtains a categorical correspondence between the complex and noncommutative tori.

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