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Revista Matemática Iberoamericana

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Volume 37, Issue 5, 2021, pp. 1897–1916
DOI: 10.4171/rmi/1252

Published online: 2021-03-03

Bing meets Sobolev

Jani Onninen[1] and Pekka Pankka[2]

(1) Syracuse University, USA and University of Jyväskylä, Finland
(2) University of Helsinki, Finland

We show that, for each $1\le p < 2$, there exists a wild involution $\mathbb{S}^3\to \mathbb{S}^3$ in the Sobolev class $W^{1,p}(\mathbb{S}^3,\mathbb{S}^3)$.

Keywords: Fixed point set, Sobolev homeomorphism, wild involution

Onninen Jani, Pankka Pekka: Bing meets Sobolev. Rev. Mat. Iberoam. 37 (2021), 1897-1916. doi: 10.4171/rmi/1252