Periods of continuous maps on closed surfaces

The objective of the present work is to present what information on the set of periodic points of a continuous self–map on a closed surface can be obtained using the action of this map on the homological groups of the closed surface.The first author of this work was partially supported by MICINN/FEDER grant number MTM2011–22587, Junta de Comunidades de Castilla-La Mancha, grant number PEII09-0220-0222. The second author was partially supported by MICINN/FEDER grant number MTM2008-03437, AGAUR grant number 2014SGR 568, ICREA Academia, FP7-PEOPLE-2012-IRSES numbers 316338 and 318999, and FEDER-UNAB10-4E-378