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Fibrations of locally symmetric spaces and the failure of the Jordan-Hölder property

Author: F. E. A. Johnson
Journal: Proc. Amer. Math. Soc. 98 (1986), 287-293
MSC: Primary 22E40; Secondary 20E15, 32L25, 55R10
MathSciNet review: 854035
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Abstract: We construct examples of locally symmetric spaces which fibre, with both base space and fibre also locally symmetric, in two distinct ways so that neither fibre nor base of one is homeomorphic to either fibre or base of the other. The simplest example is a complex surface which fibres over a complex curve in two essentially distinct ways.

In consequence, the Jordan-Hölder property fails for large classes of irreducible discrete subgroups of Lie groups.

References [Enhancements On Off] (What's this?)

  • [1] R. Bieri and B. Eckmann, Groups with homological duality generalising Poincaré duality, Invent. Math. 20 (1973), 103-124. MR 0340449 (49:5204)
  • [2] A. Borel, On the automorphisms of certain subgroups of semisimple Lie groups, Algebraic Geometry, Bombay Colloquium, Oxford Univ. Press, London, 1969, pp. 43-73. MR 0259020 (41:3663)
  • [3] A. Borel and J. P. Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1974), 244-297. MR 0387495 (52:8337)
  • [4] F. E. A. Johnson, Automorphisms of direct products of groups and their geometric realisations, Math. Ann. 263 (1983), 343-364. MR 704299 (84g:20073)
  • [5] -, On the existence of irreducible lattices, Arch. Math. 43 (1984), 391-396. MR 773185 (86i:22018)
  • [6] F. E. A. Johnson and C. T. C. Wall, On groups satisfying Poincaré duality, Ann. of Math. 96 (1972), 592-598. MR 0311796 (47:358)
  • [7] G. D. Mostow, Selfadjoint groups, Ann. of Math. 62 (1955), 44-55. MR 0069830 (16:1088a)
  • [8] B. A. F. Wehrfritz, Infinite linear groups, Ergeb. Math. Grenzgeb., vol. 76, Springer-Verlag, Berlin and New York, 1973. MR 0335656 (49:436)

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Keywords: Locally symmetric space, irreducible discrete subgroup, Jordan-Hölder property
Article copyright: © Copyright 1986 American Mathematical Society

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