FIXED POINTS OF DIFFEOMORPHISMS ON NILMANIFOLDS WITH A FREE NILPOTENT FUNDAMENTAL GROUP

被引：4

作者：

Dekimpe, Karel ^{[1
]}

Tertooy, Sam ^{[1
]}

Vargas, Antonio R. ^{[2
]}

机构：

[1] Katholieke Univ Leuven, Campus Kulak Kortrijk,E Sabbelaan 53, B-8500 Kortrijk, Belgium

[2] Katholieke Univ Leuven, Dept Math, Celestijnenlaan 200B, B-3000 Leuven, Belgium

来源：

ASIAN JOURNAL OF MATHEMATICS | 2020年 / 24卷 / 01期

关键词：

Fixed point theory; Nielsen number; Reidemeister number; free nilpotent group; nilmanifold; NIELSEN; NUMBERS; MAPS; NIL;

D O I：

10.4310/ajm.2020.v24.n1.a6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M be a nilmanifold with a fundamental group which is free 2-step nilpotent on at least 4 generators. We will show that for any nonnegative integer n there exists a self-diffeomorphism h(n) of M such that h(n), has exactly n fixed points and any self-map f of M which is homotopic to h(n) has at least n fixed points. We will also shed some light on the situation for less generators and also for higher nilpotency classes.

引用

页码：147 / 164

页数：18

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