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Elementary Quotients of Abelian Groups, and Singular Homology on Manifolds

Published online by Cambridge University Press:  22 January 2016

Marston Morse  and
Stewart Scott Cairns
Marston Morse
Affiliation:
Institute for Advanced Study, Princeton, New Jersey
Stewart Scott Cairns
Affiliation:
University of Illinois, Urbana, Illinois
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Let there be given a compact topological manifold Mn. If Mn admits a “triangulation” it is known that the fundamental invariants, namely the connectivities of Mn over fields, the Betti numbers and torsion coefficients over Z of the singular homology groups of Mn, are finite and calculable. However it is not known that a “triangulation” of Mn always exists when n > 3.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 39 , August 1970 , pp. 167 - 198
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

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