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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 S 3 which fail to generalize to the group of a knotted sphere in S 4; 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 S 3 and in S 4, with examples to show that they are not quite the same. Some special consideration will be given to regions that are the complements in S 3 or in S 4 of a finite number of tamely imbedded manifolds of co-dimension 2, and, more generally, to regions that are the complements of subcomplexes in S 3 or in S 4.

Information

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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