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On the Groups of Cobordism Ωk

Published online by Cambridge University Press:  22 January 2016

Masahisa Adachi
Masahisa Adachi*
Affiliation:
Mathematical Institute, Nagoya University
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In the papers [11] and [18] Rohlin and Thom have introduced an equivalence relation into the set of compact orientable (not necessarily connected) differentiable manifolds, which, roughly speaking, is described in the following manner: two differentiable manifolds are equivalent (cobordantes), when they together form the boundary of a bounded differentiable manifold. The equivalence classes can be added and multiplied in a natural way and form a graded algebra Ω relative to the addition, the multiplication and the dimension of manifolds. The precise structures of the groups of cobordism Ωk of dimension k are not known thoroughly. Thom [18] has determined the free part of Ω and also calculated explicitly Ωk for 0 ≦ k ≦ 7.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 13 , June 1958 , pp. 135 - 156
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1958

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