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Finite type invariants of rational homology $3$–spheres

Delphine Moussard
Algebraic & Geometric Topology 12 (2012) 2389–2428
DOI: 10.2140/agt.2012.12.2389
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.

Keywords
homology sphere, homology handlebody, Lagrangian-preserving surgery, Borromean surgery, finite type invariant, Jacobi diagram
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57N10, 57N65
References
Publication
Received: 7 March 2012
Revised: 10 August 2012
Accepted: 10 August 2012
Published: 16 January 2013
Authors
Delphine Moussard
Institut Fourier
100 rue des maths, BP 74
38402 St. Martin d’Hères Cedex
France