Any surface of genus at least 2 admits a metric locally modeled on the hyperbolic plane, and in fact it admits many such metrics. These metric structures play a fundamental roles in the study of surfaces and more in general in low-dimensional topology.
Learning objective
In the first few meetings, we will briefly review the hyperbolic plane and then construct hyperbolic metrics. I will then propose a few topics related to hyperbolic metrics and we will decide which one to pursue.
