Fixed point properties of nilpotent group actions on 1-arcwise connected continua

Fixed point properties of nilpotent group actions on 1-arcwise connected continua
HTML articles powered by AMS MathViewer

by Enhui Shi and Binyong Sun PDF

Proc. Amer. Math. Soc. 137 (2009), 771-775 Request permission

We show that every continuous action of a nilpotent group on a 1-arcwise connected continuum has at least one fixed point.

References

R. H. Bing, The elusive fixed point property, Amer. Math. Monthly 76 (1969), 119–132. MR 236908, DOI 10.2307/2317258
W. Holsztyński, Fixed points of arcwise connected spaces, Fund. Math. 64 (1969), 289–312. MR 248757, DOI 10.4064/fm-64-3-289-312
J. R. Isbell, Commuting mappings of trees, Bull. Amer. Math. Soc. 63 (1957), 419.
Roman Mańka, On uniquely arcwise connected curves, Colloq. Math. 51 (1987), 227–238. MR 891291, DOI 10.4064/cm-51-1-227-238
Roman Mańka, On spirals and fixed point property, Fund. Math. 144 (1994), no. 1, 1–9. MR 1271474, DOI 10.4064/fm-144-1-1-9
Lee Mohler, The fixed point property for homeomorphisms of $1$-arcwise connected continua, Proc. Amer. Math. Soc. 52 (1975), 451–456. MR 391064, DOI 10.1090/S0002-9939-1975-0391064-8
Peter Walters, An introduction to ergodic theory, Graduate Texts in Mathematics, vol. 79, Springer-Verlag, New York-Berlin, 1982. MR 648108
G. S. Young, Fixed-point theorems for arcwise connected continua, Proc. Amer. Math. Soc. 11 (1960), 880–884. MR 117711, DOI 10.1090/S0002-9939-1960-0117711-2