Calculation of Nielsen periodic numbers on infra-solvmanifolds

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-09-19 DOI:10.1016/j.topol.2024.109073

Changbok Li

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引用次数: 0

Abstract

Recently, a formula for computing the Nielsen periodic numbers

N F_{n} (f)

and

N P_{n} (f)

of self maps f on infra-nilmanifolds and infra-solvmanifolds of type (R) was found. In this paper, we extend this formula to the case of general infra-solvmanifolds. We show that infra-solvmanifolds are essentially reducible to the GCD and essentially toral, and determine conditions under which

N F_{n} (f) = N (f^{n})

. We show that the prime Nielsen-Jiang periodic number

N P_{n} (f)

of a self map f on an infra-solvmanifold M can be calculated by Nielsen numbers of lifts of suitable iterates of f to an

NR

-solvmanifold that finitely covers M.

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下溶漫游体上尼尔森周期数的计算

最近，我们发现了一个公式，用于计算下零曼形和下溶曼形上自映射 f 的尼尔森周期数 NFn(f) 和 NPn(f)。在本文中，我们将这一公式推广到一般的下溶点。我们证明了下溶漫游体本质上可还原为 GCD，本质上是环状的，并确定了 NFn(f)=N(fn) 的条件。我们证明了下溶漫性 M 上自映射 f 的素数尼尔森-蒋周期数 NPn(f) 可以通过 f 向有限覆盖 M 的 NR 溶漫性的合适迭代的提升的尼尔森数来计算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.