The theta divisor and the Casson-Walker invariant

Abstract

We use Heegaard decompositions and the theta divisor on a Riemannian surface to define a three-manifold invariant for rational homology three-spheres. This invariant is defined on the set of $Spi{n}^c$ structures $$\hat{\theta }:Spi{n}^c(Y)⟶Q.$$ In the first part of the paper, we give the definition of the invariant (which builds on the theory developed in the article, "The theta divisor and three-manifold invariants"). In the second part, we establish a relationship between this invariant and the Casson-Walker invariant.

50 pages, 3 figures