2012/02/14 by Patrice Le Calvez, Calvez, Patrice Le · 1 citation
Mathematics · #37B45 #37E30 #37E45 #Advanced Combinatorial Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DS #math.GT #msc:37B45 #msc:37E30 #msc:37E45
paper · pdf · doi:10.48550/arxiv.1202.3106
40 pages
arxiv created 2012/02/14 · openalex publication_date 2012/02/14 · arxiv updated 2012/02/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Some years ago, V. Markovic proved that there is no section of the Mapping Class Group for a closed surface of genus g larger than 5 (in the case of homeomorphims) and more recently generalized this result with D. Saric to the case where g is larger than 1. We will state a periodicity criterion and will use it to simplify some of the arguments given by Markovic and Saric in the proof of their theorem. The periodicity criterion tells us that a homeomorphism of a connected surface must be periodic if the set of connected periodic open sets generates the topology of the surface.