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Imbedding and isotopy of spheres in manifolds

Published online by Cambridge University Press:  24 October 2008

J. Levine
J. Levine
Affiliation:
Department of Mathematics, Cambridge
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Extract

1. The following results are special cases of theorems of Irwin and Zeeman, respectively (see (4), (9), (10)).

(a) Let V be a (2n − m + 1)−connected piecewise-linear m−manifold (bounded or not), where m − n ≥ 3. Then any element of πn(V) can be represented by a piecewise-linear imbedding of Sn in V.

(b) Let M be a (2n − m + l)-connected closed piecewise-linear (m − 1)-manifold, where m − n ≥ 3. Then two piecewise linear imbeddings of Sn−1 in V are isotopic if and only if they are homotopic.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 3 , July 1964 , pp. 433 - 437
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

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