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A Special Class of Nilmanifolds Admitting an Anosov Diffeomorphism

Karel Dekimpe and Wim Malfait
Proceedings of the American Mathematical Society
Vol. 128, No. 7 (Jul., 2000), pp. 2171-2179
Stable URL: http://www.jstor.org/stable/119713
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Special Class of Nilmanifolds Admitting an Anosov Diffeomorphism
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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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