On periodic self-homeomorphisms of closed orientable surfaces determined by their orders (Q314646)

The paper under review studies cyclic actions \(G\) on a closed orientable topological surface \(X\) of genus \(g\geq 2\). In particular, \(G\) is assumed to be a triangle group and \(X / G\) is a sphere. The authors give a classification result for the action to be \textit{weakly rigid}. This notion is defined as follows: \(G\) is weakly rigid if and only if any other cyclic action of the same order with the same orbit genus and structure of singular orbits implies there is a topological conjugacy between the actions. The conclusion of this result is a list of possible cases that can occur and the authors conclude the paper with some examples and discussion of further directions of research.