Contractible Hilbert cube manifolds
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- by T. A. Chapman
- Proc. Amer. Math. Soc. 35 (1972), 254-258
- DOI: https://doi.org/10.1090/S0002-9939-1972-0300313-0
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Abstract:
In this note we give an example of a contractible Hilbert cube manifold which cannot be embedded as an open subset of the Hilbert cube Q so that its complement (in Q) lies in a face of the boundary of Q. This example provides a negative answer to a question raised by the author.References
- R. D. Anderson, T. A. Chapman and R. M. Schori, Problems in the topology of infinite-dimensional spaces and manifolds, ZW—report, Department of Pure Mathematics, Mathematical Center, Amsterdam, 1971.
- R. H. Bing, Necessary and sufficient conditions that a $3$-manifold be $S^{3}$, Ann. of Math. (2) 68 (1958), 17–37. MR 95471, DOI 10.2307/1970041
- T. A. Chapman, On the structure of Hilbert cube manifolds, Compositio Math. 24 (1972), 329–353. MR 305432
- T. A. Chapman, Hilbert cube manifolds, Bull. Amer. Math. Soc. 76 (1970), 1326–1330. MR 286138, DOI 10.1090/S0002-9904-1970-12660-X
- T. A. Chapman, On some applications of infinite-dimensional manifolds to the theory of shape, Fund. Math. 76 (1972), no. 3, 181–193. MR 320997, DOI 10.4064/fm-76-3-181-193 M. H. A. Newman and J. H. C. Whitehead, On the group of a certain linkage, Quart. J. Math. 8 (1937), 14-21. J. H. C. Whitehead, A certain open manifold whose group is unity, Quart. J. Math. 6 (1935), 268-279.
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 254-258
- MSC: Primary 58B05; Secondary 57A20
- DOI: https://doi.org/10.1090/S0002-9939-1972-0300313-0
- MathSciNet review: 0300313