Nielsen theory on 3-manifolds covered by S
2 × ℝ |
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Authors: | Daciberg Gonçalves Peter Wong Xue Zhi Zhao |
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Institution: | 1. Dept. de Matemática-IME-USP, Caixa Postal 6;
6. 281-CEP 05314-970, São Paulo-SP, Brasil;
2. Department of Mathematics, Bates College, Lewiston, ME 04240, U.S.A.;
3. Department of Mathematics & Institute of Mathematics and Interdisciplinary Science, Capital Normal University, Beijing 100048, P. R. China |
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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 S2×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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Keywords: | Lefschetz number Nielsen number 3-manifolds |
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