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.
New series in the Johnson cokernels of the mapping class groups of surfaces
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abstract
In the present paper, we study the Sp-module structure of the cokernel of the Johnson homomorphism of the mapping class groups of surfaces. We detect the Sp-irreducible components with highest weight [1^k] (and [k]) in the cokernel. We also show that the multiplicities of them is equal to one.
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One-dimensionality of certain cocycles for the detection of the Johnson cokernel
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.