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Relative resolutions of homology manifolds

Published online by Cambridge University Press:  14 November 2011

Nigel Martin
Nigel Martin
Affiliation:
Department of Mathematics, Science Laboratories, University of Durham, Durham
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Synopsis

In the theory of resolutions of polyhedral homology manifolds to PL manifolds, itis natural to ask whether, when such a resolution exists, it is possible to preserve a given subspace of the original homology manifold under the resolution. The answer is provided in the affirmative so long as the codimension of the subspace is at least 3. In addition, it is shown that if the original dimension was at least 5 then a resolution may be chosen so as to induce an isomorphism of fundamental groups. As a corollary to these results we see that any homology n-manifold homology n-sphere may be PL embedded in S+3.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 1-2 , 1981 , pp. 43 - 47
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

1Kervaire, M. A.. Smooth homology spheres and their fundamental groups. Trans. Amer. Math. Soc. 144 (1969), 67–72.CrossRefGoogle Scholar
2Martin, N.. On the difference between homology and piecewise-linear bundles. J. London. Math. Soc. 6 (1973), 197–204.CrossRefGoogle Scholar