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

 

A special class of nilmanifolds
admitting an Anosov diffeomorphism


Authors: Karel Dekimpe and Wim Malfait
Journal: Proc. Amer. Math. Soc. 128 (2000), 2171-2179
MSC (1991): Primary 58F15, 57R50, 20F34, 20F18
Published electronically: November 23, 1999
MathSciNet review: 1664349
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Abstract: A nilmanifold admits an Anosov diffeomorphism if and only if its fundamental group (which is finitely generated, torsion-free and nilpotent) supports an automorphism having no eigenvalues of absolute value one. Here we concentrate on nilpotency class 2 and fundamental groups whose commutator subgroup is of maximal torsion-free rank. We prove that the corresponding nilmanifold admits an Anosov diffeomorphism if and only if the torsion-free rank of the abelianization of its fundamental group is greater than or equal to 3.


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Additional Information

Karel Dekimpe
Email: Karel.Dekimpe@kulak.ac.be

Wim Malfait
Email: Wim.Malfait@kulak.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05337-X
PII: S 0002-9939(99)05337-X
Keywords: Anosov diffeomorphism, nilmanifold, free 2-step nilpotent Lie algebra, hyperbolic automorphism
Received by editor(s): August 5, 1998
Published electronically: November 23, 1999
Additional Notes: Both authors are Postdoctoral Fellows of the Fund for Scientific Research – Flanders (Belgium) (F.W.O.).
Communicated by: Józef Dodziuk
Article copyright: © Copyright 2000 American Mathematical Society