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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Homotopy groups of compact Hausdorff spaces with trivial shape


Author: James E. Felt
Journal: Proc. Amer. Math. Soc. 44 (1974), 500-504
MSC: Primary 54C56; Secondary 55E05
MathSciNet review: 0346736
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Abstract: Given a collection $ \{ {\pi _n}:n = 1,2, \cdots \} $ of countable groups such that $ {\pi _i}$ is abelian and admits $ {\pi _1}$ as a group of operators for $ i \geqq 2$, we construct here an arcwise connected compact metric space of trivial shape whose $ j$th homotopy group is isomorphic to $ {\pi _j}$ for $ j = 1,2, \cdots $ . The isomorphisms preserve the action of the first group on the higher groups. Thus, the homotopy groups of a compact metric space of trivial shape may be quite arbitrary.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0346736-7
PII: S 0002-9939(1974)0346736-7
Keywords: Shape, homotopy group, shape group
Article copyright: © Copyright 1974 American Mathematical Society