## Homotopy groups of compact Hausdorff spaces with trivial shape

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- by James E. Felt
- Proc. Amer. Math. Soc.
**44**(1974), 500-504 - DOI: https://doi.org/10.1090/S0002-9939-1974-0346736-7
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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.## References

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## Bibliographic Information

- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**44**(1974), 500-504 - MSC: Primary 54C56; Secondary 55E05
- DOI: https://doi.org/10.1090/S0002-9939-1974-0346736-7
- MathSciNet review: 0346736