Abstract
Let f : M → M be a self-map of a closed manifold M of dimension dim M ≥ 3. The Nielsen number N(f) of f is equal to the minimal number of fixed points of f′ among all self-maps f′ in the homotopy class of f. In this paper, we determine N(f) for all self-maps f when M is a closed 3-manifold with S 2 × ℝ geometry. The calculation of N(f) relies on the induced homomorphisms of f on the fundamental group and on the second homotopy group of M.
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The first author was supported in part by Projeto Tematico Topologia Algebrica Geometrica e Differencial 2008/57607-6. The third author was supported in part by NSFC (Grant No. 10931005) and a project of Beijing Municipal Education Commission (Grant No. KZ201310028030)
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Gonçalves, D., Wong, P. & Zhao, X.Z. Nielsen theory on 3-manifolds covered by S 2 × ℝ. Acta. Math. Sin.-English Ser. 31, 615–636 (2015). https://doi.org/10.1007/s10114-015-3742-6
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DOI: https://doi.org/10.1007/s10114-015-3742-6