We consider the rational vector space generated by all rational homology spheres up to orientation-preserving homeomorphism, and the filtration defined on this space by Lagrangian-preserving rational homology handlebody replacements. We identify the graded space associated with this filtration with a graded space of augmented Jacobi diagrams.
"Finite type invariants of rational homology $3$–spheres." Algebr. Geom. Topol. 12 (4) 2389 - 2428, 2012. https://doi.org/10.2140/agt.2012.12.2389