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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Expanding maps on infra-nilmanifolds of homogeneous type


Authors: Karel Dekimpe and Kyung Bai Lee
Journal: Trans. Amer. Math. Soc. 355 (2003), 1067-1077
MSC (2000): Primary 37D20; Secondary 17B30, 17B70
Published electronically: October 24, 2002
MathSciNet review: 1938746
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Abstract: In this paper we investigate expanding maps on infra-nilmanifolds. Such manifolds are obtained as a quotient $E\backslash L$, where $L$ is a connected and simply connected nilpotent Lie group and $E$is a torsion-free uniform discrete subgroup of $L {\mathbb o} C$, with $C$ a compact subgroup of $\operatorname{Aut}(L)$. We show that if the Lie algebra of $L$ is homogeneous (i.e., graded and generated by elements of degree 1), then the corresponding infra-nilmanifolds admit an expanding map. This is a generalization of the result of H. Lee and K. B. Lee, who treated the 2-step nilpotent case.


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Additional Information

Karel Dekimpe
Affiliation: Katholieke Universiteit Leuven Campus Kortrijk, Universitaire Campus, B-8500 Kortrijk, Belgium
Email: Karel.Dekimpe@kulak.ac.be

Kyung Bai Lee
Affiliation: University of Oklahoma, Norman, Oklahoma 73019
Email: kblee@math.ou.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03084-2
PII: S 0002-9947(02)03084-2
Keywords: Infra-nilmanifold, expanding map, homogeneous Lie group
Received by editor(s): December 11, 2000
Received by editor(s) in revised form: March 15, 2002
Published electronically: October 24, 2002
Article copyright: © Copyright 2002 American Mathematical Society