A periodicity criterion and the section problem on the Mapping Class Group

Details A periodicity criterion and the section problem on the Mapping Class Group A periodicity criterion and the section problem on the Mapping Class Group

2012-02-14

arxiv.org/abs/1202.3106v1

Mathematics

Dynamical Systems

40 pages

Scientific paper

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.

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