Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Homology of real algebraic varieties and morphisms to spheres

Author(s): Ali Öztürk
Journal: Proc. Amer. Math. Soc. 137 (2009), 505-509.
MSC (2000): Primary 14P25; Secondary 14P05
Posted: September 15, 2008
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: Let $ X$ and $ Y$ be affine nonsingular real algebraic varieties. One of the classical problems in real algebraic geometry is whether a given $ C^\infty$ mapping $ f:X\rightarrow Y$ can be approximated by entire rational mappings in the space of $ C^\infty$ mappings. In this work, we obtain some sufficient conditions in the case when $ Y$ is the standard sphere $ S^n$.

References:

1.
S. Akbulut, H. King, Topology of Real Algebraic Sets, M.S.R.I. book series (Springer, New York, 1992). MR 1225577 (94m:57001)

2.
J. Bochnak, M. Coste, M.F. Roy, Real Algebraic Geometry, Ergebnisse der Math., vol. 36 (Springer, Berlin, 1998). MR 1659509 (2000a:14067)

3.
J. Bochnak and W. Kucharz, On real algebraic morphisms into even-dimensional spheres, Ann. of Math. (2), 128 (1988) 415-433. MR 960952 (89k:57060)

4.
J. Bochnak, M. Buchner and W. Kucharz, Vector bundles over real algebraic varieties, $ K$-Theory, 3 (1990) 271-298. MR 1040403 (91b:14075)

5.
J. Bochnak and W. Kucharz, Algebraic approximation of mappings into spheres, Michigan Math. J., 34 (1987) 119-125. MR 873026 (88h:58018)

6.
J. Bochnak and W. Kucharz, Complex cycles on real algebraic models of a smooth manifold, Proc. Amer. Math. Soc., 114 (1992) 1097-1104. MR 1093594 (93g:57032)

7.
J. Bochnak and W. Kucharz, Algebraic models of smooth manifolds, Invent. Math., 97 (1989) 585-611. MR 1005007 (91b:14076)

8.
G.E. Bredon, Topology and Geometry (Springer, New York, 1993). MR 1224675 (94d:55001)

9.
N. Ivanov, Approximation of smooth manifolds by real algebraic sets, Russian Math. Surveys, 37 (1982) 1-59. MR 643764 (84i:57029)

10.
J. L. Loday, Applications algébriques du tore dans la sphère et de $ S^p\times S^q$ dans $ S^{p+q}$, Lect. Notes in Math 342 (Springer, 1973). MR 0368034 (51:4276)

11.
Y. Ozan, On entire rational maps in real algebraic geometry, Michigan Math. J., 42 (1995) 141-145. MR 1322195 (96b:14070)

12.
Y. Ozan, On homology of real algebraic varieties, Proc. Amer. Math. Soc., 129 (2001) 3167-3175. MR 1844989 (2002m:14048)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14P25, 14P05

Retrieve articles in all Journals with MSC (2000): 14P25, 14P05

Additional Information:

Ali Öztürk
Affiliation: Department of Mathematics, Abant Izzet Baysal University, 14280 Bolu, Turkey
Email: ozturkali@ibu.edu.tr

DOI: 10.1090/S0002-9939-08-09600-7
PII: S 0002-9939(08)09600-7
Keywords: Real algebraic varieties, algebraic homology, regular morphisms
Received by editor(s): November 10, 2005,
Received by editor(s) in revised form: March 2, 2008
Posted: September 15, 2008
Communicated by: Ted Chinburg
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google