Homology and orientation reversing periodic maps on surfaces

2016/03/01 by Haibin Hang, Hang, Haibin
Mathematics · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1603.00507

openalex publication_date 2016/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a classification of orientation reversing periodic maps on closed surfaces which generalizes the theory of Nielsen for the orientation preserving periodic maps. On one hand, we give a group of data for each orientation reversing periodic map such that two periodic maps with the same data must be conjugate to each other. On the other hand, we give the criterion to judge when two different groups of data correspond to the same conjugacy class. As an application of the results of this paper, we shall show that a given orientation reversing periodic map on Σ_g with period larger than or equal to 3g must be conjugate to the power of a list of particular types of periodic maps.

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