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On the Torelli Lie algebra

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arxiv 2106.16010 v2 pith:TPXZMMAW submitted 2021-06-30 math.AT math.GT

Alexander Kupers , Oscar Randal-Williams This is my paper · ORCID
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keywords algebratorelliassociatedcentreconsistsgenusgrouphomomorphism
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abstract

We prove two theorems about the Malcev Lie algebra associated to the Torelli group of a surface of genus $g$: stably, it is Koszul and the kernel of the Johnson homomorphism consists only of trivial $Sp_{2g}(\mathbb{Z})$-representations lying in the centre.

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  1. One-dimensionality of certain cocycles for the detection of the Johnson cokernel

    math.AT 2025-07 accept novelty 4.0 of 10

    The vertex-graded 1-cocycles of the ribbon graph complex RGC1 are one-dimensional and spanned by the graph G1 corresponding to the Enomoto-Satoh trace.

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