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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Nielsen numbers of maps of tori

Authors: Robin B. S. Brooks, Robert F. Brown, Jingyal Pak and Douglas H. Taylor
Journal: Proc. Amer. Math. Soc. 52 (1975), 398-400
MSC: Primary 55C20
MathSciNet review: 0375287
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Abstract: The main result states that if $f:X \to X$ is any map on a $k$-dimensional torus $X$, then the Nielsen number and Lefschetz number of $f$ are related by the formula $N(f) = |L(f)|$. Thus, on the torus, the Lefschetz number gives information, not just on the existence of fixed points, but on the number of fixed points as well. No other compact Lie group has this property. The main result, when applied to certain types of maps on compact Lie groups, produces new information on the fixed point theory of such maps.

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Keywords: Nielsen number, Lefschetz number, fixed point, compact Lie group, homogeneous space
Article copyright: © Copyright 1975 American Mathematical Society