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

 

Nielsen numbers of periodic maps on solvmanifolds


Author: Kyung Bai Lee
Journal: Proc. Amer. Math. Soc. 116 (1992), 575-579
MSC: Primary 55M20; Secondary 57R15
MathSciNet review: 1123659
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Abstract: Let $ f:M \to M$ be a self-map of a solvmanifold $ M$. Then the Lefschetz number $ L(f)$ and the Nielsen number $ N(f)$ of $ f$ satisfy $ \vert L(f)\vert \leq N(f)$. If $ f$ is homotopically periodic (i.e., $ {f^k} \simeq {\text{id}}$, for some $ k \geq 1$), then $ L(f) = N(f)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1123659-8
PII: S 0002-9939(1992)1123659-8
Keywords: Lefschetz number, Nielsen number, homotopically periodic map, solvmanifold, nilmanifold, flat manifold
Article copyright: © Copyright 1992 American Mathematical Society