A complex which cannot be pushed around in 𝐸³

Starbird, Michael

doi:10.1090/S0002-9939-1977-0442945-X

A complex which cannot be pushed around in $E^{3}$
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Proc. Amer. Math. Soc. 63 (1977), 363-367 Request permission

Abstract:

This paper contains an example of a finite complex C with triangulation T which admits two linear embeddings f and g into ${E^3}$ so that although there is an isotopy of ${E^3}$ taking the embedding f to g there is no continuous family of linear embeddings of C starting at f and ending at g. No such example can exist in ${E^2}$.

References

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R. H. Bing and Michael Starbird, Linear isotopies in $E^{2}$, Trans. Amer. Math. Soc. 237 (1978), 205–222. MR 461510, DOI 10.1090/S0002-9947-1978-0461510-7
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Opera postuma

Chung Wu Ho, On certain homotopy properties of some spaces of linear and piecewise linear homeomorphisms. I, II, Trans. Amer. Math. Soc. 181 (1973), 213–233; ibid. 181 (1973), 235–243. MR 322891, DOI 10.1090/S0002-9947-1973-0322891-3
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