(Joint with logic) Two models for the hyperbolic plane and existence of the Poincaré metric on compact Riemann surfaces

Seminar series

Number Theory Seminar

Date

Thu, 12 May 2016
16:00

Location

Speaker

Norbert A’Campo

Organisation

University of Basel

An implicite definition for the hyperbolic plane $H=H_I$ is in: ${\rm Spec}(\mathbb{R}[X]) = H_I \cup \mathbb{R}$. All geometric hyperbolic features will follow from this definition in an elementary way.

A second definition is $H=H_J=\{J \in {\rm End}(R^2) \mid J^2=-Id, dx \wedge dy(u,Ju) \geq 0 \}$. Working with $H=H_J$ allows to prove rather directly main theorems about Riemann surfaces.