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Proceedings of the American Mathematical Society

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Linear isotopies in $ E\sp{3}$

Author: Michael Starbird
Journal: Proc. Amer. Math. Soc. 65 (1977), 342-346
MSC: Primary 57A10; Secondary 57A35
MathSciNet review: 0454982
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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 [Enhancements On Off] (What's this?)

  • [1] R. H. Bing, An alternative proof that 3-manifolds can be triangulated, Ann. of Math. (2) 69 (1959), 37-65. MR 0100841 (20:7269)
  • [2] R. H. Bing and M. Starbird, Linear isotopies in $ {E^2}$, Trans. Amer. Math. Soc. (to appear). MR 0461510 (57:1495)
  • [3] S. S. Cairns, Isotopic deformations of geodesic complexes on the 2-sphere and plane, Ann. of Math. (2) 45 (1944), 207-217. MR 0010271 (5:273d)
  • [4] M. Starbird, A complex which cannot be pushed around in $ {E^3}$, Proc. Amer. Math. Soc. 63 (1977), 363-367. MR 0442945 (56:1320)

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Keywords: Linear isotopy, linear embeddings
Article copyright: © Copyright 1977 American Mathematical Society

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