2004/08/23 by Jerome Levine, Levine, Jerome
Mathematics · #57M25 #57N10 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA #msc:57M25 #msc:57N10
paper · pdf · doi:10.48550/arxiv.math/0408310
12 pages, 1 figure
arxiv created 2004/08/23 · arxiv updated 2009/12/01
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.