On periodic self-homeomorphisms of closed orientable surfaces determined by their orders.

The fundamentals for the topological classification of periodic orientation-preserving self-homeomorphisms of a closed orientable topological surface X of genus $$g \ge 2$$ have been established, by Nielsen, in the thirties of the last century. Here we consider two concepts related to this classification; rigidity and weak rigidity. A cyclic action G of order N on X is said to be topologically rigid if any other cyclic action of order N on X is topologically conjugate to it. If this assertion holds for arbitrary other action but having, in addition, the same orbit genus and the same structure of singular orbits, then G is said to be weakly topologically rigid. We give a precise description of rigid and weakly rigid cyclic quasi-platonic actions which mean actions having three singular orbits and for which X / G is a sphere. [ABSTRACT FROM AUTHOR]