Non-separating immersions of spheres and Bing houses

Freedman, Michael; Nguễyn-Phan, T. Tâm

doi:10.4310/MRL.2021.v28.n4.a5

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Non-separating immersions of spheres and Bing houses

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Nguễyn-Phan, T. Tâm
Max Planck Institute for Mathematics, Max Planck Society;

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https://dx.doi.org/10.4310/MRL.2021.v28.n4.a5
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https://doi.org/10.48550/arXiv.1911.08858
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Citation

Freedman, M., & Nguễyn-Phan, T. T. (2021). Non-separating immersions of spheres and Bing houses. Mathematical Research Letters, 28(4), 1085-1106. doi:10.4310/MRL.2021.v28.n4.a5.

Cite as: https://hdl.handle.net/21.11116/0000-0009-B8E9-1

Abstract

n all dimensions n≥4 we construct explicit non-separating, locally flat, PL immersions of Sn−1↬Sn. In fact, the complement of these immersions is diffeomorphic to Rn. These generalize the famous “house with two rooms” or “Bing house” which is an immersion S2↬R3⊂S3.