Mathematical Research Letters

Volume 28 (2021)

Number 4

Approximation rigidity and $h$-principle for Bing spines

Pages: 1107 – 1123



Michael Freedman (Microsoft Research, Station Q; and Department of Mathematics, University of California, Santa Barbara, Calif., U.S.A.)

T. Tâm Nguễyn-Phan (Max Planck Institut für Mathematik, Bonn, Germany)


We show that all $\mathsf{PL}$ manifolds of dimension $\geq 3$ have spines similar to Bing’s house with two rooms. Beyond this we explore approximation rigidity and an $h$-principle.

Received 23 January 2020

Accepted 5 February 2021

Published 22 November 2021