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By James Conant, Rob Schneiderman and Peter Teichner


In his study of the group of homology cylinders, J. Levine [19] made the conjecture that a certain homomorphism η ′ : T → D ′ is an isomorphism. Here T is an abelian group on labeled oriented trees, and D ′ is the kernel of a bracketing map on a quasi-Lie algebra. Both T and D ′ have strong connections to a variety of topological settings, including the mapping class group, homology cylinders, finite type invariants, Whitney tower intersection theory, and the homology of Out(Fn). In this paper, we confirm Levine’s conjecture. This is a central step in classifying the structure of links up to grope and Whitney tower concordance, as explained in other papers of this series [1, 2, 3, 4]. We also confirm and improve upon Levine’s conjectured relation between two filtrations of the group of homology cylinders

Year: 2010
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