2014
DOI: 10.2140/agt.2014.14.627
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New series in the Johnson cokernels of the mapping class groups of surfaces

Abstract: Let Σ g,1 be a compact oriented surface of genus g with one boundary component, and M g,1 its mapping class group. Morita showed that the image of the k-th Johnson homomorphism τ M k of M g,1 is contained in the kernel h g,1 (k) of an Sp-equivariant surjective homomorphism H ⊗ Z L 2g (k + 1) → L 2g (k + 2), where H := H 1 (Σ g,1 , Z) and L 2g (k) is the degree k-part of the free Lie algebra L 2g generated by H.In this paper, we study the Sp-module structure of the cokernelIn particular, we show that the irredu… Show more

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Cited by 27 publications
(61 citation statements)
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“…Combining Hain's result above and the fact that Coker(τ We wrote down a maximal vector of [1 k ] in [17]. In [49], Nakamura and Tsunogai gave a table of the Sp-irreducible decompositions of h Q g,1 (k) for 1 ≤ k ≤ 15, which are calculated by a computer.…”
Section: Now Let Us Recall the Fact That The Image Of τmentioning
confidence: 99%
“…Combining Hain's result above and the fact that Coker(τ We wrote down a maximal vector of [1 k ] in [17]. In [49], Nakamura and Tsunogai gave a table of the Sp-irreducible decompositions of h Q g,1 (k) for 1 ≤ k ≤ 15, which are calculated by a computer.…”
Section: Now Let Us Recall the Fact That The Image Of τmentioning
confidence: 99%
“…The Lie algebra a g appeared in a recent work of Enomoto and Satoh [6] and also in Kawazumi and Kuno [13], where they found certain new roles of this Lie algebra. We refer to the above cited papers for details.…”
Section: Discussionmentioning
confidence: 94%
“…Generalizing the trace maps, Enomoto and Satoh [23] found more components in the cokernel of τ Q . Different approaches to the cokernel were given by Conant-Kassabov-Vogtmann [17] and Kawazumi-Kuno [53].…”
Section: Theorem 53 (Morita [73]) the Homomorphismmentioning
confidence: 90%