The theta divisor and the Casson-Walker invariant

Details The theta divisor and the Casson-Walker invariant The theta divisor and the Casson-Walker invariant

2000-06-26

arxiv.org/abs/math/0006194v1

Mathematics

Geometric Topology

50 pages, 3 figures

Scientific paper

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 $Spin^c$ structures $$ {\hat \theta}\colon Spin^c(Y)\longrightarrow Q. $$ 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.

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