We define an invariant of rational homology 3-spheres via vector fields. The construction of our invariant is a generalization of both that of the Kontsevich-Kuperberg-Thurston invariant and that of Watanabe's Morse homotopy invariant, which implies the equivalence of these two invariants.
The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant
3-cobordisms with their rational homology on the boundary
Splitting formulae for the Kontsevich-Kuperberg-Thurston invariant of rational homology 3-spheres
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