Noncommutative geometry of algebraic curves

Author:
Igor V. Nikolaev

Journal:
Proc. Amer. Math. Soc. **137** (2009), 3283-3290

MSC (2000):
Primary 14H10, 46L40, 58F10

DOI:
https://doi.org/10.1090/S0002-9939-09-09917-1

Published electronically:
May 7, 2009

MathSciNet review:
2515397

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A covariant functor from the category of generic complex algebraic curves to a category of the -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 -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:
https://doi.org/10.1090/S0002-9939-09-09917-1

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.