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.Comment: 40 page