2013/09/18 by Hooper, W. Patrick
#06B23 (Secondary) #30F30 #32G15 #37E99 #57M50 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1309.4795
We define a moduli space of translation structures on the open topological disk with a basepoint and endow it with a locally-compact metrizable topology. We call this the immersive topology, because it is defined using the concept of immersions: continuous maps between subsets of translation surfaces that respect the basepoints and the translation structures. Immersions induce a partial ordering on the moduli space, and we prove the ordering is nearly a complete lattice in the sense of order theory: The space is only missing a minimal element. Subsequent articles will uncover more structure and develop a topology on the space of all translation structures.