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• W3102269475 abstract "In his study of the group of homology cylinders, J. Levine made the conjecture that a certain homomorphism eta': 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 the group of automorphisms of the free group. 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. We also confirm and improve upon Levine's conjectured relation between two filtrations of the group of homology cylinders." @default.
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• W3102269475 date "2012-04-08" @default.
• W3102269475 modified "2023-09-26" @default.
• W3102269475 title "Tree homology and a conjecture of Levine" @default.
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• W3102269475 doi "https://doi.org/10.2140/gt.2012.16.555" @default.
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