Propagators associated with Morse functions. A formula for the Theta-invariant of framed 3-manifolds from Heegaard diagrams.

The Theta-invariant of a framed rational homology 3-sphere is the sum of the Casson-Walker invariant and a Pontrjagin number associated with the framing. It can be defined as the algebraic intersection of three $4$-dimensional chains, called propagators, in a configuration space. I shall describe explicit propagators associated with Morse functions coming from Heegaard diagrams (constructed with G. Kuperberg),
and present a combinatorial formula for the Theta-invariant from Heegaard diagrams.