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On the equivalence of several definitions of compact infra-solvmanifolds. (English) Zbl 1288.22006

The authors show the equivalence of five definitions of compact infra-solvmanifolds that appear in the literature.

MSC:

22E25 Nilpotent and solvable Lie groups
22E40 Discrete subgroups of Lie groups
53C30 Differential geometry of homogeneous manifolds
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References:

[1] O. Baues, Infra-solvmanifolds and rigidity of subgroups in solvable linear algebraic groups, Topology 43 (2004), no. 4, 903-924. · Zbl 1059.57022 · doi:10.1016/j.top.2003.11.002
[2] F. T. Farrell and L. E. Jones, Classical aspherical manifolds , CBMS Regional Conference Series in Mathematics, 75, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1990. · Zbl 0729.57001
[3] F. T. Farrell and L. E. Jones, Compact infrasolvmanifolds are smoothly rigid, in Geometry from the Pacific Rim (Singapore, 1994) , 85-97, de Gruyter, Berlin, 1997. · Zbl 0895.53047
[4] J. Hilgert and K.-H. Neeb, Structure and geometry of Lie groups , Springer Monographs in Mathematics, Springer, New York, 2012. · Zbl 1229.22008
[5] K. H. Hofmann and S. A. Morris, The structure of compact groups , second revised and augmented edition, de Gruyter Studies in Mathematics, 25, de Gruyter, Berlin, 2006.
[6] P. A. Smith, Fixed-point theorems for periodic transformations, Amer. J. Math. 63 (1941), 1-8. · Zbl 0024.19004 · doi:10.2307/2371271
[7] W. Tuschmann, Collapsing, solvmanifolds and infrahomogeneous spaces, Differential Geom. Appl. 7 (1997), no. 3, 251-264. · Zbl 0885.53043 · doi:10.1016/S0926-2245(96)00054-X
[8] B. Wilking, Rigidity of group actions on solvable Lie groups, Math. Ann. 317 (2000), no. 2, 195-237. · Zbl 0957.22009 · doi:10.1007/s002089900091
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