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Nielsen numbers of homotopically periodic maps on infrasolvmanifolds

Author: Christopher K. McCord
Journal: Proc. Amer. Math. Soc. 120 (1994), 311-315
MSC: Primary 55M20; Secondary 57N65
MathSciNet review: 1240025
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Abstract: A well-known lower bound for the number of fixed points of a self-map $ f:X \to X$ is the Nielsen number $ N(f)$. Unfortunately, the Nielsen number is difficult to calculate. The Lefschetz number $ L(f)$, on the other hand, is readily computable but usually does not estimate the number of fixed points. In this paper, we show that on infrasolvmanifolds (aspherical manifolds whose fundamental group has a normal solvable group of finite index), $ N(f) = L(f)$ when $ f$ is a homotopically periodic map.

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