2013/10/19 by W. Patrick Hooper, Hooper, W. Patrick
Computer Science · #32G15 #37D50 (Secondary) #37E99 #57M50 (Primary) 30F30 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1310.5193
openalex publication_date 2013/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A translation structure on a surface is an atlas of charts to the plane so that the transition functions are translations. We allow our surfaces to be non-compact and infinite genus. We endow the space of all pointed surfaces equipped with a translation structure with a topology, which we call the immersive topology because it is related to the manner in which disks can be immersed into such a surface. We prove that a number of operations typically done to translation surfaces are continuous with respect to the topology. We show that the topology is Hausdorff, and that the collection of surfaces with a fixed lower bound on the injectivity radius at the basepoint is compact.