Lectures on Vector Bundles Over Riemann Surfaces

Lectures on Vector Bundles Over Riemann Surfaces Synopsis

These notes are based on a course of lectures given at Princeton University during the academic year 1966-1967. The topic is the analytic theory of complex vector bundles over compact Riemann surfaces. It begins with a general discussion of complex analytic vector bundles over compact Riemann surfaces from the point of view of sheaf theory.

It goes on to discuss a descriptive classification of complex analytic vector bundles of rank 2 on a compact Riemann surface and follows with a discussion of flat vector bundles over compact Riemann surfaces. Two appendices cover some questions that arise.