$6$-dimensional manifolds without totally algebraic homology
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- by Peter Teichner PDF
- Proc. Amer. Math. Soc. 123 (1995), 2909-2914 Request permission
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
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Additional Information
- © Copyright 1995 American Mathematical Society
- 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