An invariant of rational homology $3$–spheres via vector fields

Abstract

We give an alternative construction of the Kontsevich–Kuperberg–Thurston invariant for rational homology $3$–spheres. This construction is a generalization of the original construction of the Kontsevich–Kuperberg–Thurston invariant. As an application, we give a Morse homotopy theoretic description of the Kontsevich–Kuperberg–Thurston invariant (close to a description by Watanabe).