Nielsen numbers of homotopically periodic maps on infrasolvmanifolds

McCord, Christopher K.

doi:10.1090/S0002-9939-1994-1240025-7

Nielsen numbers of homotopically periodic maps on infrasolvmanifolds
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by Christopher K. McCord

Proc. Amer. Math. Soc. 120 (1994), 311-315

DOI: https://doi.org/10.1090/S0002-9939-1994-1240025-7

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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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