Annals of Functional Analysis

Riemann surfaces and AF-algebras

Igor Nikolaev

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For a generic set in the Teichmüller 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. In the special case of genus one, one gets a functor between the category of complex tori and the Effros–Shen algebras.

Article information

Ann. Funct. Anal., Volume 7, Number 2 (2016), 371-380.

Received: 13 August 2015
Accepted: 3 November 2015
First available in Project Euclid: 8 April 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L85: Noncommutative topology [See also 58B32, 58B34, 58J22]
Secondary: 14H55: Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]

Riemann surfaces $\mathit{AF}$-algebras


Nikolaev, Igor. Riemann surfaces and $\mathit{AF}$ -algebras. Ann. Funct. Anal. 7 (2016), no. 2, 371--380. doi:10.1215/20088752-3544893.

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