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

 

Rigid $ 3$-dimensional compacta whose squares are manifolds


Authors: Fredric D. Ancel, Paul F. Duvall and S. Singh
Journal: Proc. Amer. Math. Soc. 88 (1983), 330-332
MSC: Primary 54G20; Secondary 54B15, 55M15, 57P99
MathSciNet review: 695269
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Abstract: A space is rigid if its only self-homeomorphism is the identity. In response to a question of Jan van Mill, Ancel and Singh have given examples of rigid $ n$-dimensional compacta, for each $ n \geqslant 4$, whose squares are manifolds. We construct a rigid $ 3$-dimensional compactum whose square is the manifold $ {S^3} \times {S^3}$. In fact, we construct uncountably many topologically distinct compacta with these properties.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0695269-2
PII: S 0002-9939(1983)0695269-2
Keywords: Cell-like compactum, homogeneous, manifold, generalized $ 3$-manifold, cell-like decomposition
Article copyright: © Copyright 1983 American Mathematical Society