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Proceedings of the American Mathematical Society
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
MathSciNet review: 1264830
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1264830-7
PII: S 0002-9939(1995)1264830-7
Article copyright: © Copyright 1995 American Mathematical Society