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PL-Submanifolds and Homology Classes of a PL-Manifold*)

Published online by Cambridge University Press:  22 January 2016

Masahisa Adachi
Masahisa Adachi*
Affiliation:
Mathematical Institute, Nagoya University
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This paper is devoted to the problem of the realisation of homology classes of a PL-manifold by PL-submanifolds.

The present study is founded on the consideration of Thorn complexes M(PLk), M(SPLk) for PL-microbundles which is defined by R. Williamson [5]. We shall apply Thom’s method [4] to PL-manifolds.

The author is grateful to Professors R. Shizuma and K. Shiraiwa for their kind criticisms.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 29 , March 1967 , pp. 69 - 74
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

Footnotes

*)

This work is partially supported by Yukawa Fellowship.

References

[1] Kister, J., Microbedies are fibre bundles, Ann. of Math., 80 (1964), 190–199.Google Scholar
[2] Milnor, J., Lectures Lracteristic classes, Mimeographed Note, Princeton University, 1957–58.Google Scholar
[3] Milnor, J., Microbundles and differentiable structures, Mimeographed Note, Princeton University, 1961.Google Scholar
[4] Thom, R., Quelques propriétés globales des variétés différentiables, Comment. Math. Helv., 28 (1954), 17–86.Google Scholar
[5] Williamson, R., Cobordism of combinatorial manifolds, Ann. of Math., 83 (1966), 1–33.Google Scholar