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Rigid finite-dimensional compacta whose squares are manifolds

Authors: Fredric D. Ancel and S. Singh
Journal: Proc. Amer. Math. Soc. 87 (1983), 342-346
MSC: Primary 54G20; Secondary 55M15, 57P99
MathSciNet review: 681845
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Abstract: A space is rigid if its only self-homeomorphism is the identity. We answer questions of Jan van Mill by constructing for each $ n$, $ 4 \leqslant n < \infty $, a rigid $ n$-dimensional compactum whose square is homogeneous because it is a manifold. Moreover, for each $ n$, $ 4 \leqslant n < \infty $, we give uncountably many topologically distinct such examples. Infinite-dimensional examples are also given.

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Keywords: Generalized $ n$-manifold, decomposition spaces, homology spheres, homogeneous, cell-like decomposition
Article copyright: © Copyright 1983 American Mathematical Society

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