Actions of finitely generated groups on the universal Menger curve
HTML articles powered by AMS MathViewer
- by Kazuhiro Kawamura PDF
- Proc. Amer. Math. Soc. 130 (2002), 609-611 Request permission
Abstract:
We prove that every finitely generated group acts effectively on the universal Menger curve.References
- R. D. Anderson, A characterization of the universal curve and a proof of its homogeneity, Ann. of Math. (2) 67 (1958), 313–324. MR 96180, DOI 10.2307/1970007
- R. D. Anderson, One-dimensional continuous curves and a homogeneity theorem, Ann. of Math. (2) 68 (1958), 1–16. MR 96181, DOI 10.2307/1970040
- R. D. Anderson, The algebraic simplicity of certain groups of homeomorphisms, Amer. J. Math. 80 (1958), 955–963. MR 98145, DOI 10.2307/2372842
- 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
- Alex Chigogidze, Kazuhiro Kawamura, and E. D. Tymchatyn, Menger manifolds, Continua (Cincinnati, OH, 1994) Lecture Notes in Pure and Appl. Math., vol. 170, Dekker, New York, 1995, pp. 37–88. MR 1326834
- A. N. Dranishnikov, Free actions of $0$-dimensional compact groups, Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), no. 1, 212–228 (Russian); English transl., Math. USSR-Izv. 32 (1989), no. 1, 217–232. MR 936531, DOI 10.1070/IM1989v032n01ABEH000755
- Y. Iwamoto and K. Sakai, The homeomorphism group of the universal Menger compactum is simple, preprint.
- Kazuhiro Kawamura, A survey on Menger manifold theory—update, Topology Appl. 101 (2000), no. 1, 83–91. MR 1730898, DOI 10.1016/S0166-8641(98)00124-2
- J. C. Mayer, Lex G. Oversteegen, and E. D. Tymchatyn, The Menger curve. Characterization and extension of homeomorphisms of non-locally-separating closed subsets, Dissertationes Math. (Rozprawy Mat.) 252 (1986), 45. MR 874232
- J. C. Mayer and C. W. Stark, Group actions on Menger manifolds, preprint.
- Katsuro Sakai, Free actions of zero-dimensional compact groups on Menger manifolds, Proc. Amer. Math. Soc. 122 (1994), no. 2, 647–648. MR 1249889, DOI 10.1090/S0002-9939-1994-1249889-4
- Vlad Sergiescu and Takashi Tsuboi, Acyclicity of the groups of homeomorphisms of the Menger compact spaces, Amer. J. Math. 118 (1996), no. 6, 1299–1312. MR 1420925
Additional Information
- Kazuhiro Kawamura
- Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
- MR Author ID: 255566
- Email: kawamura@math.tsukuba.ac.jp
- Received by editor(s): February 10, 2000
- Received by editor(s) in revised form: August 8, 2000
- Published electronically: June 19, 2001
- Communicated by: Alan Dow
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 609-611
- MSC (2000): Primary 57S05, 54F50
- DOI: https://doi.org/10.1090/S0002-9939-01-06089-0
- MathSciNet review: 1862145