The Theta Divisor and Three-Manifold Invariants

Abstract

In this paper we study an invariant for oriented three-manifolds with $b_1>0$, which is defined using Heegaard splittings and the theta divisor of a Riemann surface. The paper is divided into two parts, the first of which gives the definition of the invariant, and the second of which identifies it with more classical (torsion) invariants of three-manifolds. Its close relationship with Seiberg-Witten theory is also addressed.