All autohomeomorphisms of connected Menger manifolds are stable

Sakai, Katsuro

doi:10.1090/S0002-9939-1994-1273522-9

All autohomeomorphisms of connected Menger manifolds are stable
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Proc. Amer. Math. Soc. 122 (1994), 1289-1291 Request permission

Abstract:

Generalizing the result of Chigogidze (1991), we prove that all autohomeomorphisms of connected Menger manifolds are stable (in the sense of Brown and Gluck).

References

Czesław Bessaga and Aleksander Pełczyński, Selected topics in infinite-dimensional topology, Monografie Matematyczne, Tom 58. [Mathematical Monographs, Vol. 58], PWN—Polish Scientific Publishers, Warsaw, 1975. MR 0478168
Mladen Bestvina, Characterizing $k$-dimensional universal Menger compacta, Mem. Amer. Math. Soc. 71 (1988), no. 380, vi+110. MR 920964, DOI 10.1090/memo/0380
Morton Brown and Herman Gluck, Stable structures on manifolds. I. Homeomorphisms of $S^{n}$, Ann. of Math. (2) 79 (1964), 1–17. MR 158383, DOI 10.2307/1970481
T. A. Chapman, Lectures on Hilbert cube manifolds, Regional Conference Series in Mathematics, No. 28, American Mathematical Society, Providence, R.I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975. MR 0423357

Autohomeomorphisms of the universal Menger compacta are stable

142 (3)

A. Chigogidze, Finding a boundary for a Menger manifold, Proc. Amer. Math. Soc. 121 (1994), no. 2, 631–640. MR 1231030, DOI 10.1090/S0002-9939-1994-1231030-5
D. W. Curtis and R. A. McCoy, Stable homeomorphisms on infinite-dimensional normed linear spaces, Proc. Amer. Math. Soc. 28 (1971), 496–500. MR 283831, DOI 10.1090/S0002-9939-1971-0283831-2
Sze-tsen Hu, Theory of retracts, Wayne State University Press, Detroit, 1965. MR 0181977

A mapping theorem for Q-manifolds and

manifolds

R. A. McCoy, Groups of homeomorphisms of normed linear spaces, Pacific J. Math. 39 (1971), 735–743. MR 309151
Katsuro Sakai, On $\textbf {R}^{\infty }$-manifolds and $Q^{\infty }$-manifolds, Topology Appl. 18 (1984), no. 1, 69–79. MR 759140, DOI 10.1016/0166-8641(84)90032-4
Katsuro Sakai, On $\textbf {R}^{\infty }$-manifolds and $Q^{\infty }$-manifolds. II. Infinite deficiency, Tsukuba J. Math. 8 (1984), no. 1, 101–118. MR 747449, DOI 10.21099/tkbjm/1496159948
Raymond Y. T. Wong, A note on stable homeomorphisms of infinite-dimensional manifolds, Proc. Amer. Math. Soc. 28 (1971), 271–272. MR 271996, DOI 10.1090/S0002-9939-1971-0271996-8