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All autohomeomorphisms of connected Menger manifolds are stable


Author: Katsuro Sakai
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
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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 [Enhancements On Off] (What's this?)

  • [BP] C. Bessaga and A. Pełczyński, Selected topics in infinite-dimensional topology, Monograf. Mat., vol. 58, Polish Sci. Publ., Warsaw, 1975. MR 0478168 (57:17657)
  • [Be] M. Bestvina, Characterizing k-dimensional universal Menger compacta, Mem. Amer. Math. Soc. (no.380) 71 (1988). MR 920964 (89g:54083)
  • [BG] M. Brown and H. Gluck, Stable structures on manifolds: I, II, III, Ann. of Math. (2) 79 (1964), 1-58. MR 0158383 (28:1608a)
  • [Ch] T. A. Chapman, Lectures on Hilbert cube manifolds, CBMS Regional Conf. Ser. in Math., vol. 28, Amer. Math. Soc., Providence, RI, 1976. MR 0423357 (54:11336)
  • [C$ _{1}$] A. Chigogidze, Autohomeomorphisms of the universal Menger compacta are stable, Soobshch Akad. Nauk Gruz. SSR 142 (3) (1991), 477-479.
  • [C$ _{2}$] -, Finding boundaries for Menger manifolds, Proc. Amer. Math. Soc. 121 (1994), 631-640. MR 1231030 (94k:57038)
  • [CM] D. Curtis and R. A. McCoy, Stable homeomorphisms on infinite-dimensional normed linear spaces, Proc. Amer. Math. Soc. 28 (1971), 496-500. MR 0283831 (44:1061)
  • [Hu] S.-T. Hu, Theory of retracts, Wayne State Univ. Press, Detroit, MI, 1965. MR 0181977 (31:6202)
  • [IS] Y. Iwamoto and K. Sakai, A mapping theorem for Q-manifolds and $ {\mu ^{n + 1}}$-manifolds, preprint.
  • [Mc] R. A. McCoy, Groups of homeomorphisms of normed linear spaces, Pacific J. Math. 39 (1971), 735-743. MR 0309151 (46:8261)
  • [S$ _{1}$] K. Sakai, On $ {\mathbb{R}^\infty }$-manifolds and $ {Q^\infty }$-manifolds, Topology Appl. 18 (1984), 69-80. MR 759140 (86a:57014)
  • [S$ _{2}$] -, On $ {\mathbb{R}^\infty }$-manifolds and $ {Q^\infty }$-manifolds, II: Infinite deficiency, Tsukuba J. Math. 8 (1984), 101-118. MR 747449 (86i:57021)
  • [Wo] R. Y. T. Wong, A note on stable homeomorphisms of infinite-dimensional manifolds, Proc. Amer. Math. Soc. 28 (1971), 271-272. MR 0271996 (42:6877)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1273522-9
Keywords: Autohomeomorphism, Menger manifold, stable
Article copyright: © Copyright 1994 American Mathematical Society

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