All autohomeomorphisms of connected Menger manifolds are stable
HTML articles powered by AMS MathViewer
- by Katsuro Sakai
- Proc. Amer. Math. Soc. 122 (1994), 1289-1291
- DOI: https://doi.org/10.1090/S0002-9939-1994-1273522-9
- PDF | 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 A. Chigogidze, Autohomeomorphisms of the universal Menger compacta are stable, Soobshch Akad. Nauk Gruz. SSR 142 (3) (1991), 477-479.
- 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 Y. Iwamoto and K. Sakai, A mapping theorem for Q-manifolds and ${\mu ^{n + 1}}$-manifolds, preprint.
- 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
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 1289-1291
- MSC: Primary 57N20; Secondary 54F15, 57N99
- DOI: https://doi.org/10.1090/S0002-9939-1994-1273522-9
- MathSciNet review: 1273522