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Which Abelian Groups Can be Fundamental Groups of Regions in Euclidean Spaces?

Published online by Cambridge University Press:  20 November 2018

Bai Ching Chang
Bai Ching Chang*
Affiliation:
Princeton University, Princeton, New Jersey
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It is known that there are a lot of properties of the group of a knot in S3 which fail to generalize to the group of a knotted sphere in S4; among them are included Dehn's lemma, Hopf's conjecture, and the aspherity of knots. In this paper, we shall investigate the properties of the fundamental groups of regions in S3 and in S4, with examples to show that they are not quite the same. Some special consideration will be given to regions that are the complements in S3 or in S4 of a finite number of tamely imbedded manifolds of co-dimension 2, and, more generally, to regions that are the complements of subcomplexes in S3 or in S4.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 7 - 18
Copyright
Copyright © Canadian Mathematical Society 1974

References

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