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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

[1] Anosov, D. V., The Nielsen numbers of maps of nil-manifolds, Uspehi Mat. Nauk, 40 (1985), 133–134; Russian Math. Survey, 40 (1985), 149–150.Google Scholar
[2] Jiang, B., Lectures on Nielsen fixed point theory, Contemporary Mathematics 14, American Mathematical Society, Providence, R.I., 1983.Google Scholar
[3] Lee, J. B. and Lee, K. B., Lefschetz numbers for continuous maps, and periods for expanding maps on infra-nilmanifolds, preprint (2003).Google Scholar
[4] Lee, K. B., Maps on infra-nilmanifolds, Pacific J. Math., 168 (1995), 157–166.Google Scholar
[5] McCord, C. K., Estimating Nielsen numbers on infrasolvmanifolds, Pacific J. Math., 154 (1992), 345–368.Google Scholar
[6] Shin, J., Isometry groups of unimodular simply connected 3-dimensional Lie groups, Geom. Dedicata, 65 (1997), 267–290.Google Scholar