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On a Homology Theory Associated to Foliations

Published online by Cambridge University Press:  22 January 2016

Yoshihiro Shikata
Yoshihiro Shikata*
Affiliation:
Mathematical Institute, Nagoya University
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In this note, we associate a foliated singular homology theory to a foliation on a compact manifold X and construct a spectral sequence which relates the foliated homology to the ordinary homology of X. Since the foliated homology is so constructed as to be related closely to a certain topological behavior of the foliation, we may expect that further study of the spectral sequence reveals some information on topology of foliation. The study and applications will be given in a sequel.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 38 , March 1970 , pp. 53 - 61
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Bredon, G., Cosheaves and homology, Pacific J. of Math. Vol. 25, (1968), 1–32.Google Scholar
[2] Cartan, H. and Eilenberg, S., Homological algebra, Princeton Univ. Press, (1956).Google Scholar
[3] Reeb, G., Sur les espaces fibrés et les varietes feuilletées, Actualités scientifiques et industrielles, Hermann Paris, n° 1183.Google Scholar
[4] Spanier, E., Algebraic topology, McGraw-Hill, (1966).Google Scholar