A special class of nilmanifolds admitting an Anosov diffeomorphism
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- by Karel Dekimpe and Wim Malfait PDF
- Proc. Amer. Math. Soc. 128 (2000), 2171-2179 Request permission
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.References
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Additional Information
- Karel Dekimpe
- Email: Karel.Dekimpe@kulak.ac.be
- Wim Malfait
- Email: Wim.Malfait@kulak.ac.be
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2171-2179
- MSC (1991): Primary 58F15, 57R50, 20F34, 20F18
- DOI: https://doi.org/10.1090/S0002-9939-99-05337-X
- MathSciNet review: 1664349