Homeomorphisms of Hilbert cube manifolds

Chapman, T. A.

doi:10.1090/S0002-9947-1973-0372863-8

Homeomorphisms of Hilbert cube manifolds
HTML articles powered by AMS MathViewer

by T. A. Chapman

Trans. Amer. Math. Soc. 182 (1973), 227-239

DOI: https://doi.org/10.1090/S0002-9947-1973-0372863-8

PDF | Request permission

Abstract:

It is shown in this paper that the homeomorphism group of any compact Hubert cube manifold is locally contractible. The proof uses some standard infinite-dimensional techniques along with an infinite-dimensional version of the torus-homeomorphism idea which was used by Edwards and Kirby to establish a corresponding finite-dimensional result.

References

R. D. Anderson, On topological infinite deficiency, Michigan Math. J. 14 (1967), 365–383. MR 214041, DOI 10.1307/mmj/1028999787
R. D. Anderson and R. Schori, Factors of infinite-dimensional manifolds, Trans. Amer. Math. Soc. 142 (1969), 315–330. MR 246327, DOI 10.1090/S0002-9947-1969-0246327-5
Richard Arens, Topologies for homeomorphism groups, Amer. J. Math. 68 (1946), 593–610. MR 19916, DOI 10.2307/2371787

Some properties of certain subsets of infinite-dimensional spaces

Morton Brown, Locally flat imbeddings of topological manifolds, Ann. of Math. (2) 75 (1962), 331–341. MR 133812, DOI 10.2307/1970177
T. A. Chapman, Dense sigma-compact subsets of infinite-dimensional manifolds, Trans. Amer. Math. Soc. 154 (1971), 399–426. MR 283828, DOI 10.1090/S0002-9947-1971-0283828-7
T. A. Chapman, On the structure of Hilbert cube manifolds, Compositio Math. 24 (1972), 329–353. MR 305432
T. A. Chapman, Canonical extensions of homeomorphisms, General Topology and Appl. 2 (1972), 227–247. MR 310826, DOI 10.1016/0016-660X(72)90009-8
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

Topological invariance of Whitehead torsion

Robert D. Edwards and Robion C. Kirby, Deformations of spaces of imbeddings, Ann. of Math. (2) 93 (1971), 63–88. MR 283802, DOI 10.2307/1970753
J. F. P. Hudson, Piecewise linear topology, W. A. Benjamin, Inc., New York-Amsterdam, 1969. University of Chicago Lecture Notes prepared with the assistance of J. L. Shaneson and J. Lees. MR 0248844
R. C. Kirby and L. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742–749. MR 242166, DOI 10.1090/S0002-9904-1969-12271-8
James E. West, Infinite products which are Hilbert cubes, Trans. Amer. Math. Soc. 150 (1970), 1–25. MR 266147, DOI 10.1090/S0002-9947-1970-0266147-3
Raymond Y. T. Wong, On homeomorphisms of certain infinite dimensional spaces, Trans. Amer. Math. Soc. 128 (1967), 148–154. MR 214040, DOI 10.1090/S0002-9947-1967-0214040-4