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On Realising Mod-2 Homology Classes of Manifolds by Submanifolds

Published online by Cambridge University Press:  20 January 2009

Stavros Papastavridis
Stavros Papastavridis
Affiliation:
University of Athens, Mathematical Institute, Solonos 57, Athens 143, Greece
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In his fundamental paper (3), Thorn proved, among other things, that a mod-2 homology class of an n-dimensional, closed, compact, C∞ manifold, which has dimension n/2, can be realised by a submanifold, (see (3), Théorème II. 1 and Corollaire 11.13).

In this note we examine the question of realisability of mod-2 homology classes of the next higher dimension.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 2 , June 1979 , pp. 109 - 111
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

(1) Brown, E. and Peterson, F., Relations among characteristic classes I, Topology 3 (Supplement 1) (1964), 39–52.CrossRefGoogle Scholar
(2) Ledden, P. J., Nonstable homotopy groups of Thorn complexes, Proc. Amer. Math. Soc. 29(1971), 404–410.CrossRefGoogle Scholar
(3) Thom, R., Quelques propriétès globales des variétés differentiables, Comm. Math. Helv. 28 (1954), 17–86.CrossRefGoogle Scholar