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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Noncommutative geometry of algebraic curves


Author: Igor V. Nikolaev
Journal: Proc. Amer. Math. Soc. 137 (2009), 3283-3290
MSC (2000): Primary 14H10, 46L40, 58F10
Published electronically: May 7, 2009
MathSciNet review: 2515397
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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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Additional Information

Igor V. Nikolaev
Affiliation: The Fields Institute for Mathematical Sciences, Toronto, Ontario, M5T 3J1, Canada
Address at time of publication: 101–315 Holmwood Avenue, Ottawa, Ontario, K1S 2R2, Canada
Email: igor.v.nikolaev@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09917-1
PII: S 0002-9939(09)09917-1
Keywords: Complex algebraic curves, $C^*$-algebras
Received by editor(s): September 5, 2008
Received by editor(s) in revised form: February 13, 2009
Published electronically: May 7, 2009
Additional Notes: The author was partially supported by NSERC
Communicated by: Varghese Mathai
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.