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Submanifolds of real algebraic varieties
Author(s):
W.
Kucharz
Journal:
Proc. Amer. Math. Soc.
136
(2008),
55-60.
MSC (2000):
Primary 14P05, 14C25
Posted:
September 25, 2007
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Abstract:
By the Nash-Tognoli theorem, each compact smooth manifold  is diffeomorphic to a nonsingular real algebraic set, called an algebraic model of  . We construct algebraic models  of  with controlled behavior of the group of cohomology classes represented by algebraic subsets of  .
References:
-
- 1.
- S. Akbulut and H. King, Topology of Real Algebraic Sets, Math. Sci. Research Institute Publ. 25, Springer, 1992. MR 1225577 (94m:57001)
- 2.
- J. Bochnak, M. Coste and M.-F. Roy, Real Algebraic Geometry, Ergebnisse der Math. und ihrer Grenzgeb. Folge (3), Vol. 36, Springer, 1998. MR 1659509 (2000a:14067)
- 3.
- J. Bochnak and W. Kucharz, On homology classes represented by real algebraic varieties, Banach Center Publications 44 (1998), 21-35. MR 1677394 (2000b:14080)
- 4.
- J. Bochnak and W. Kucharz, On approximation of smooth submanifolds by nonsingular real algebraic subvarieties, Ann. Sci. Ec. Norm. Sup. 36 (2003), 685-690. MR 2032984 (2004j:14063)
- 5.
- A. Borel and A. Haefliger, La classe d'homologie fondamentale d'un espace analytique, Bull. Soc. Math. France 89 (1961), 461-513. MR 0149503 (26:6990)
- 6.
- G. Bredon, Topology and Geometry, New York, Berlin, Heidelberg, Springer, 1997. MR 1700700 (2000b:55001)
- 7.
- P. Conner, Differentiable Periodic Maps, Lecture Notes in Math. Vol. 738, Springer, 1979. MR 548463 (81f:57018)
- 8.
- J. Huisman and F. Mangolte, Every orientable Seifert
 -manifold is a real component of a uniruled algebraic variety, Topology 44 (2005), 63-71. MR 2104001 (2005h:14139) - 9.
- J. Kollár, The topology of real and complex algebraic varieties, Taniguchi Conference on Mathematics, Nara 1998, Advanced Studies in Pure Mathematics, Vol. 31, Mathematical Society of Japan, Tokyo, 2001, pp. 127-145. MR 1865090 (2003a:14033)
- 10.
- W. Kucharz, Algebraic equivalence and homology classes of algebraic cycles, Math. Nachr. 180 (1996), 135-140. MR 1397672 (97e:14009)
- 11.
- W. Kucharz, Algebraic cycles and algebraic models of smooth manifolds, J. Algebraic Geometry 11 (2002), 101-127. MR 1865915 (2002j:14065)
- 12.
- J. Nash, Real algebraic manifolds, Ann. of Math. 56 (1952), 405-421. MR 0050928 (14:403b)
- 13.
- R. Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17-86. MR 0061823 (15:890a)
- 14.
- A. Tognoli, Su una congettura di Nash, Ann. Scuola Norm. Sup. Pisa, Sci. Fis. Mat. 27 (3) (1973), 167-185. MR 0396571 (53:434)
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Additional Information:
W.
Kucharz
Affiliation:
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131-1141
Email:
kucharz@math.unm.edu
DOI:
10.1090/S0002-9939-07-08944-7
PII:
S 0002-9939(07)08944-7
Received by editor(s):
September 10, 2005
Received by editor(s) in revised form:
September 28, 2006
Posted:
September 25, 2007
Communicated by:
Paul Goerss
Copyright of article:
Copyright
2007,
American Mathematical Society
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