2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72255In a recent paper we defined a new filtration of the mapping class group--the "Lagrangian" filtration. We here determine the successive quotients of this filtration, up to finite index. As an application we show that, for any additive invariant of finite-type (e.g. the Casson invariant), and any level of the Lagrangian filtration, there is a homology 3-sphere which has a Heegaard decomposition whose gluing diffeomorphism lies at that level, on which this invariant is non-zero. In a final section we examine the relationship between the Johnson and Lagrangian filtrations.12 pages, 1 figureGeometric TopologyQuantum Algebra57N10; 57M25text