An unknotting theorem in -manifolds

Author:
Vo Thanh Liem

Journal:
Proc. Amer. Math. Soc. **82** (1981), 125-132

MSC:
Primary 57N20; Secondary 57N37

DOI:
https://doi.org/10.1090/S0002-9939-1981-0603615-9

MathSciNet review:
603615

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we prove the following unknotting theorem.

Theorem. Let *be a* *-manifold and let* be a homotopy such that *and* *are* *-deficient embeddings. Then, there is an isotopy* *such that* *and* . *Moreover, if* is limited by an open cover *of* *and is stationary on a closed subset* *of* , *then we may choose* *to also be limited by* *and to be the identity on* .

However, a similar unknotting theorem for -embeddings does not hold true in and .

**[1]**T. A. Chapman,*Lectures on Hilbert cube manifolds*, CBMS Regional Conf. Ser. in Math., no. 28, Amer. Math. Soc., Providence, R. I., 1976. MR**0423357 (54:11336)****[2]**R. Geoghegan,*Open problems in infinite-dimensional topology*, 1979 (preprint). MR**583711 (82a:57015)****[3]**R. E. Heisey,*Manifolds modelled on the direct limit of Hilbert cubes*, Proc. 1977 Georgia Topology Conf., Academic Press, New York, 1979, pp. 609-619. MR**537754 (83a:57015)****[4]**R. E. Heisey and H. Torunzcyk,*On the topology of direct limits of*ANR'*s*(preprint).**[5]**V. T. Liem,*An**-approximation theorem for**-manifolds*, General Topology Appl. (to appear). MR**623737 (82k:57011)****[6]**S. Ferry,*The homeomorphism group of a compact Hilbert cube manifold is an*AR, Ann. of Math. (2)**106**(1977), 101-119. MR**0461536 (57:1521)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0603615-9

Keywords:
Hilbert cube,
direct limit space,
-set,
inductive -set,
-deficient,
isotopy,
unknotting theorem

Article copyright:
© Copyright 1981
American Mathematical Society