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Averaging Formula for Nielsen Numbers

Published online by Cambridge University Press:  11 January 2016

Seung Won Kim ,
Jong Bum lee  and
Kyung Bai Lee
Seung Won Kim
Affiliation:
Department of Mathematics, Sogang University, Seoul 121-742, Korea, swkim@sogang.ac.kr
Jong Bum lee
Affiliation:
Department of Mathematics, Sogang University, Seoul 121-742, Korea, jlee@sogang.ac.kr
Kyung Bai Lee
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, OK 73019, U.S.A., kb lee@AFTERMATH.math.ou.edu
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Abstract

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We prove that the averaging formula for Nielsen numbers holds for continuous maps on infra-nilmanifolds: Let M be an infra-nilmanifold and ƒ: M → M be a continuous map. Suppose MK is a regular covering of M which is a compact nilmanifold with π1(MK = K. Assume that f*(K) ⊂ K. Then ƒ has a lifting . We prove a question raised by McCord, which is for any with an essential fixed point class, fix =1. As a consequence, we obtain the following averaging formula for Nielsen numbers

Keywords

55M2057S30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 178 , 2005 , pp. 37 - 53
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

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