Homotopical theory of periodic points of periodic homeomorphisms on closed surfaces |
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Authors: | Wac aw Marzantowicz,Xuezhi Zhao |
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Affiliation: | aFaculty of Mathematics and Computer Sci., UAM, 61-614, Poznań, Poland;bDepartment of Mathematics & Institute of Mathematics and Interdisciplinary Science, Capital Normal University, Beijing 100048, PR China |
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Abstract: | In this work we show that the Wecken theorem for periodic points holds for periodic homeomorphisms on closed surfaces, which therefore completes the periodic point theory in such a special case. Using it we derive the set of homotopy minimal periods for such homeomorphisms. Moreover we show that the results hold for homotopically periodic self-maps of closed surfaces. This let us to re-formulate our results as a statement on properties of elements of finite order in the group of outer automorphisms of the fundamental group of a surface with non-positive Euler characteristic. |
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Keywords: | Periodic point Surface homeomorphism Nielsen number |
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