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Averaging formula for Nielsen coincidence numbers

Published online by Cambridge University Press:  11 January 2016

Seung Won Kim  and
Jong Bum Lee
Seung Won Kim
Affiliation:
School of Mathematics Korea Institute for Advanced StudySeoul 130-722Koreaswkim@kias.re.kr
Jong Bum Lee
Affiliation:
Department of Mathematics Sogang UniversitySeoul 121-742Koreajlee@sogang.ac.kr
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Abstract

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In this paper we study the averaging formula for Nielsen coincidence numbers of pairs of maps (f,g): M→N between closed smooth manifolds of the same dimension. Suppose that G is a normal subgroup of Π = π1(M) with finite index and H is a normal subgroup of Δ = π1(N) with finite index such that Then we investigate the conditions for which the following averaging formula holds

where is any pair of fixed liftings of (f, g). We prove that the averaging formula holds when M and N are orientable infra-nilmanifolds of the same dimension, and when M = N is a non-orientable infra-nilmanifold with holonomy group ℤ2 and (f, g) admits a pair of liftings on the nil-covering of M.

Keywords

55M2057S30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 186 , 2007 , pp. 69 - 93
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

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