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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0854035-8
PII: S 0002-9939(1986)0854035-8
Keywords: Locally symmetric space, irreducible discrete subgroup, Jordan-Hölder property
Article copyright: © Copyright 1986 American Mathematical Society