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The Lagrangian filtration of the mapping class group and finite-type invariants of homology spheres
Published online by Cambridge University Press: 28 September 2006
Abstract
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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 141 , Issue 2 , September 2006 , pp. 303 - 315
- Copyright
- 2006 Cambridge Philosophical Society
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