Linear isotopies in $E^{3}$
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- by Michael Starbird PDF
- Proc. Amer. Math. Soc. 65 (1977), 342-346 Request permission
Abstract:
In this paper it is shown that if f and g are two PL embeddings of a finite complex K into ${E^3}$ so that there is an orientation-preserving homeomorphism h of ${E^3}$ with $h \circ f = g$, then there is a triangulation T of K and a linear isotopy ${h_t}:(K,T) \to {E^3}(t \in [0,1])$ so that ${h_0} = f$ and ${h_1} = g$.References
- R. H. Bing, An alternative proof that $3$-manifolds can be triangulated, Ann. of Math. (2) 69 (1959), 37–65. MR 100841, DOI 10.2307/1970092
- 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
- Stewart S. Cairns, Isotopic deformations of geodesic complexes on the 2-sphere and on the plane, Ann. of Math. (2) 45 (1944), 207–217. MR 10271, DOI 10.2307/1969263
- Michael Starbird, A complex which cannot be pushed around in $E^{3}$, Proc. Amer. Math. Soc. 63 (1977), no. 2, 363–367. MR 442945, DOI 10.1090/S0002-9939-1977-0442945-X
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 342-346
- MSC: Primary 57A10; Secondary 57A35
- DOI: https://doi.org/10.1090/S0002-9939-1977-0454982-X
- MathSciNet review: 0454982