A complex which cannot be pushed around in

Author:
Michael Starbird

Journal:
Proc. Amer. Math. Soc. **63** (1977), 363-367

MSC:
Primary 57A35

MathSciNet review:
0442945

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Abstract: This paper contains an example of a finite complex *C* with triangulation *T* which admits two linear embeddings *f* and *g* into so that although there is an isotopy of 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 .

**[1]**R. H. Bing,*An alternative proof that 3-manifolds can be triangulated*, Ann. of Math. (2)**69**(1959), 37–65. MR**0100841****[2]**R. H. Bing and Michael Starbird,*Linear isotopies in 𝐸²*, Trans. Amer. Math. Soc.**237**(1978), 205–222. MR**0461510**, 10.1090/S0002-9947-1978-0461510-7**[3]**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**0010271****[4]**L. Euler,*Opera postuma*. I, Petropoli (1862), 464-496.**[5]**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**0322891**, 10.1090/S0002-9947-1973-0322891-3**[6]**Michael Starbird,*Linear isotopies in 𝐸³*, Proc. Amer. Math. Soc.**65**(1977), no. 2, 342–346. MR**0454982**, 10.1090/S0002-9939-1977-0454982-X

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1977-0442945-X

Keywords:
Linear isotopy,
push

Article copyright:
© Copyright 1977
American Mathematical Society