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Mathematical Research Letters
Volume 28 (2021)
Number 4
Non-separating immersions of spheres and Bing houses
Pages: 1085 – 1106
DOI: https://dx.doi.org/10.4310/MRL.2021.v28.n4.a5
Authors
Abstract
In all dimensions $n \geq 4$ we construct explicit non-separating, locally flat, $\mathsf{PL}$ immersions of $\mathbb{S}^{n-1} \looparrowright S^n$. In fact, the complement of these immersions is diffeomorphic to $\mathbb{R}^n$. These generalize the famous “house with two rooms” or “Bing house” which is an immersion $S^2 \looparrowright \mathbb{R}^3 \subset S^3$.
Received 23 January 2020
Accepted 5 February 2021
Published 22 November 2021