-dimensional manifolds without totally algebraic homology

Author:
Peter Teichner

Journal:
Proc. Amer. Math. Soc. **123** (1995), 2909-2914

MSC:
Primary 57R20; Secondary 57R19, 57R40, 57R95

MathSciNet review:
1264830

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We construct 6-dimensional manifolds for which not all codimension 2 homology classes (with -coefficients) are realized by algebraic subvarieties in any real algebraic structure on the manifold. It was known that such examples exist in dimension 11 and higher, and that dimension 6 is the best possible. We also give an elementary algebraic topological proof of a connection between codimension 2 submanifolds and vector bundles which was previously proven only by algebraic geometrical methods.

**[1]**R. Benedetti and M. Dedò,*Counterexamples to representing homology classes by real algebraic subvarieties up to homeomorphism*, Compositio Math.**53**(1984), no. 2, 143–151. MR**766294****[2]**J. Bochnak and W. Kucharz,*Algebraic cycles and approximation theorems in real algebraic geometry*, Trans. Amer. Math. Soc.**337**(1993), no. 1, 463–472. MR**1091703**, 10.1090/S0002-9947-1993-1091703-8**[3]**John W. Milnor and James D. Stasheff,*Characteristic classes*, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. Annals of Mathematics Studies, No. 76. MR**0440554****[4]**René Thom,*Quelques propriétés globales des variétés différentiables*, Comment. Math. Helv.**28**(1954), 17–86 (French). MR**0061823**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
57R20,
57R19,
57R40,
57R95

Retrieve articles in all journals with MSC: 57R20, 57R19, 57R40, 57R95

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1995-1264830-7

Article copyright:
© Copyright 1995
American Mathematical Society