Goldman flows on the Jacobian

TL;DR

This paper demonstrates that Goldman flows maintain the holomorphic structure of the Jacobian, a moduli space of fundamental group representations into U(1), revealing a geometric invariance under these flows.

Contribution

It establishes that Goldman flows preserve the holomorphic structure on the Jacobian, connecting geometric flows with complex structure stability.

Findings

Goldman flows preserve the holomorphic structure of the Jacobian.

The result links geometric flows to complex structure invariance.

The study focuses on the moduli space of U(1) representations.

Abstract

We show that the Goldman flows preserve the holomorphic structure on the moduli space of homomorphisms of the fundamental group of a Riemann surface into U(1), in other words the Jacobian.