Open Collections

Topologizing the space of all translation structures

Banff International Research Station for Mathematical Innovation and Discovery

I will describe a topology on the space of all translation structures on surfaces with a basepoint (including surfaces of arbitrary topological types). The topology is built in two steps. First, the space of translation structures on the open disk and the natural disk bundle over this space are given second-countable locally-compact metrizable topologies. The observation that the universal cover of a surface with a translation structure is a topological disk allows us to place a topology on the space of all translation structures. I will attempt to concentrate on the practical use of the topologies such as proving a sequence converges in this topology and consequences of such convergence.

Mathematics; Dynamical systems and ergodic theory; Algebraic geometry; Dynamical systems

video/mp4

Author affiliation: City College of New York

2017-02-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59693

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/