Finite type invariants of rational homology 3-spheres

TL;DR

This paper explores the structure of rational homology 3-spheres using a filtration based on handlebody replacements and identifies the associated graded space with augmented Jacobi diagrams, advancing understanding of their invariants.

Contribution

It establishes a correspondence between the graded space of rational homology spheres under a specific filtration and augmented Jacobi diagrams, revealing new algebraic structures.

Findings

Identification of the graded space with augmented Jacobi diagrams

Development of a filtration based on Lagrangian-preserving handlebody replacements

Enhanced understanding of finite type invariants of rational homology 3-spheres

Abstract

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.