The Lagrangian filtration of the mapping class group and finite-type invariants of homology spheres

Details The Lagrangian filtration of the mapping class group and finite-type invariants of homology spheres The Lagrangian filtration of the mapping class group and finite-type invariants of homology spheres

2004-08-23

arxiv.org/abs/math/0408310v1

Mathematics

Geometric Topology

12 pages, 1 figure

Scientific paper

In 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.

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