Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the equivalence of several definitions of compact infra-solvmanifolds

Shintarô Kuroki and Li Yu

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Abstract

We show the equivalence of several definitions of compact infra-solvmanifolds that appear in various math literatures.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 89, Number 9 (2013), 114-118.

Dates
First available in Project Euclid: 30 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.pja/1383138416

Digital Object Identifier
doi:10.3792/pjaa.89.114

Mathematical Reviews number (MathSciNet)
MR3127929

Zentralblatt MATH identifier
1288.22006

Subjects
Primary: 22E25: Nilpotent and solvable Lie groups 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 22F30: Homogeneous spaces {For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40}
Secondary: 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]

Keywords
Infra-solvmanifold solvable Lie group homogeneous space discrete group action holonomy

Citation

Kuroki, Shintarô; Yu, Li. On the equivalence of several definitions of compact infra-solvmanifolds. Proc. Japan Acad. Ser. A Math. Sci. 89 (2013), no. 9, 114--118. doi:10.3792/pjaa.89.114. https://projecteuclid.org/euclid.pja/1383138416


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References

  • O. Baues, Infra-solvmanifolds and rigidity of subgroups in solvable linear algebraic groups, Topology 43 (2004), no. 4, 903–924.
  • 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.
  • 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.
  • J. Hilgert and K.-H. Neeb, Structure and geometry of Lie groups, Springer Monographs in Mathematics, Springer, New York, 2012.
  • 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.
  • P. A. Smith, Fixed-point theorems for periodic transformations, Amer. J. Math. 63 (1941), 1–8.
  • W. Tuschmann, Collapsing, solvmanifolds and infrahomogeneous spaces, Differential Geom. Appl. 7 (1997), no. 3, 251–264.
  • B. Wilking, Rigidity of group actions on solvable Lie groups, Math. Ann. 317 (2000), no. 2, 195–237.