BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Topologizing the space of all translation structures Hooper, Patrick


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.

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