Nielsen numbers of homotopically periodic maps on infrasolvmanifolds
Nielsen numbers of homotopically periodic maps on infrasolvmanifolds
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DOI：
10.1090/s0002-9939-1994-1240025-7
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
C. McCord
中科院分区：
文献类型：
--
作者：
C. McCord
自映射f：X的不动点个数的一个众所周知的下界是→数N(F)。不幸的是，尼尔森数很难计算。另一方面，莱夫谢茨数L(F)很容易计算，但通常不估计不动点的数目。本文证明了当f是同伦周期映射时，在次可解流形(基本群具有有限指数正规可解群的非球面流形)上，N(F)=L(f
A well-known lower bound for the number of fixed points of a self-map f: X → 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