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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54G20, 54B15, 55M15, 57P99

Retrieve articles in all journals with MSC: 54G20, 54B15, 55M15, 57P99

Additional Information

Keywords: Cell-like compactum, homogeneous, manifold, generalized $ 3$-manifold, cell-like decomposition
Article copyright: © Copyright 1983 American Mathematical Society