Finite type 3-manifold invariants and the structure of the Torelli

1996/09/22 by Stavros Garoufalidis, Garoufalidis, Stavros, Jerome Levine +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9609027

52 pages, AMSLatex, 20 figures

arxiv created 1996/09/22 · openalex publication_date 1996/09/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply the theory of finite-type invariants of homology 3-spheres to investigate the structure of the Torelli group. We construct natural cocycles in the Torelli group and show that the lower central series quotients of the Torelli group map onto a vector space of trivalent graphs. We also have analogous results for two other natural subgroups of the mapping class group.

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