Rigid 3-Dimensional Compacta Whose Squares are Manifolds

Fredric D. Ancel, Paul F. Duvall, S. Singh
1983 Proceedings of the American Mathematical Society  
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 «-dimensional compacta, for each n > 4, whose squares are manifolds. We construct a rigid 3-dimensional compactum whose square is the manifold S3 X S3. In fact, we construct uncountably many topologically distinct compacta with these properties.
doi:10.2307/2044727 fatcat:bs2jq3sg55c4he4arrfocjx7x4