A lower bound for the number of group actions on a compact Riemann surface

作者：Anderson James W^*; Wootton Aaron

来源：Algebraic and Geometric Topology, 2012, 12(1): 19-35.

DOI：10.2140/agt.2012.12.19

We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus sigma %26gt;= 2 is at least quadratic in sigma. We do this through the introduction of a coarse signature space, the space K-sigma of skeletal signatures of group actions on compact Riemann surfaces of genus sigma. We discuss the basic properties of K-sigma and present a full conjectural description.

• 出版日期2012