Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

$ 6$-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
DOI: https://doi.org/10.1090/S0002-9939-1995-1264830-7
MathSciNet review: 1264830
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct 6-dimensional manifolds for which not all codimension 2 homology classes (with $ \mathbb{Z}/2$-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.


References [Enhancements On Off] (What's this?)

  • [1] R. Benedetti and M. Dedó, Counterexamples to representing homology classes by real algebraic subvarieties up to homeomorphism, Compositio Math. 53 (1984), 143-151. MR 766294 (86h:57031)
  • [2] J. Bochnak and W. Kucharz, Algebraic cycles and approximation theorems in real algebraic geometry, Trans. Amer. Math. Soc. 337 (1993), 463-472. MR 1091703 (93g:57033)
  • [3] J. Milnor and J. Stasheff, Characteristic classes, Ann. of Math. Stud., no. 76, Princeton Univ. Press, Princeton, NJ, 1974. MR 0440554 (55:13428)
  • [4] R. Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17-86. MR 0061823 (15:890a)

Similar Articles

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: https://doi.org/10.1090/S0002-9939-1995-1264830-7
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society