|
Noncommutative geometry of algebraic curves
Author(s):
Igor
V.
Nikolaev
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3283-3290.
MSC (2000):
Primary 14H10, 46L40, 58F10
Posted:
May 7, 2009
MathSciNet review:
2515397
Retrieve article in:
PDF
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.
References:
-
- 1.
- M. Bauer, A characterization of uniquely ergodic interval exchange maps in terms of the Jacobi-Perron algorithm, Bol. Soc. Bras. Mat. 27 (1996), 109-128. MR 1418928 (98a:58100)
- 2.
- L. Bernstein, The Jacobi-Perron Algorithm, Its Theory and Applications, Lect. Notes in Math., 207, Springer, 1971. MR 0285478 (44:2696)
- 3.
- A. Douady and J. Hubbard, On the density of Strebel differentials, Inventiones Math. 30 (1975), 175-179. MR 0396936 (53:796)
- 4.
- E. G. Effros, Dimensions and
 -Algebras, Conf. Board of the Math. Sciences Regional Conference Series in Math., No. 46, Amer. Math. Soc., 1981. MR 623762 (84k:46042) - 5.
- E. G. Effros and C. L. Shen, Approximately finite
 -algebras and continued fractions, Indiana Univ. Math. J. 29 (1980), 191-204. MR 563206 (81g:46076) - 6.
- G. A. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra 38 (1976), 29-44. MR 0397420 (53:1279)
- 7.
- J. Hubbard and H. Masur, Quadratic differentials and foliations, Acta Math. 142 (1979), 221-274. MR 523212 (80h:30047)
- 8.
- M. Kontsevich, XI Solomon Lefschetz Memorial Lecture Series: Hodge structures in non-commutative geometry (Notes by Ernesto Lupercio), in Contemp. Mathematics, 462, Amer. Math. Soc., 2008. MR 2444365
- 9.
- Yu. I. Manin, Real multiplication and noncommutative geometry, in ``Legacy of Niels Hendrik Abel'', 685-727, Springer, 2004. MR 2077591 (2006e:11077)
- 10.
- H. Masur, Interval exchange transformations and measured foliations, Ann. of Math. (2) 115 (1982), no. 1, 169-200. MR 644018 (83e:28012)
- 11.
- A. Polishchuk and A. Schwarz, Categories of holomorphic vector bundles on noncommutative two-tori, Commun. Math. Phys. 236 (2003), 135-159. MR 1977884 (2004k:58011)
- 12.
- Y. Soibelman and V. Vologodsky, Noncommutative compactifications and elliptic curves, Int. Math. Res. Not. (2003), 1549-1569. MR 1976601 (2004i:14017)
- 13.
- W. P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988), 417-431. MR 956596 (89k:57023)
- 14.
- W. A. Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. (2) 115 (1982), no. 1, 201-242. MR 644019 (83g:28036b)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
14H10, 46L40, 58F10
Retrieve articles in all Journals with
MSC (2000):
14H10, 46L40, 58F10
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:
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
Posted:
May 7, 2009
Additional Notes:
The author was partially supported by NSERC
Communicated by:
Varghese Mathai
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
