New series in the Johnson cokernels of the mapping class groups of surfaces

Enomoto, Naoya; Satoh, Takao

doi:10.48550/arxiv.1012.2175

Cited by 7 publications

(11 citation statements)

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“…which simultaneously generalizes the construction of Enomoto-Satoh [5] and of Conant-Kassabov-Vogtmann [3]. (The superscript "C" stands for "cokernel.")…”

Section: Introductionmentioning

confidence: 69%

“…All of the representations coming from this so-called "Galois obstruction" appear as the trivial Sp-representation [0] Sp , giving an infinite family of cokernel obstructions. Morita [12] showed that representations [k] Sp appear in the cokernel for all odd k ≥ 3, and more recently Enomoto and Satoh [5] showed that representations [1 4m+1 ] Sp appear in the cokernel as well.…”

Section: Introductionmentioning

confidence: 99%

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The Johnson cokernel and the Enomoto–Satoh invariant

Conant

2015

Algebr. Geom. Topol.

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ABSTRACT. We study the cokernel of the Johnson homomorphism for the mapping class group of a surface with one boundary component. A graphical trace map simultaneously generalizing trace maps of Enomoto-Satoh and Conant-Kassabov-Vogtmann is given, and using technology from the author's work with Kassabov and Vogtmann, this is is shown to detect a large family of representations which vastly generalizes series due to Morita and Enomoto-Satoh. The Enomoto-Satoh trace is the rank 1 part of the new trace. The rank 2 part is also investigated.

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“…which simultaneously generalizes the construction of Enomoto-Satoh [5] and of Conant-Kassabov-Vogtmann [3]. (The superscript "C" stands for "cokernel.")…”

Section: Introductionmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 99%

The Johnson cokernel and the Enomoto–Satoh invariant

Conant

2015

Algebr. Geom. Topol.

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“…Remark 7.2. 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%

Abelianizations of derivation Lie algebras of the free associative algebra and the free Lie algebra

Morita,

Sakasai,

Suzuki

2011

Preprint

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We determine the abelianizations of the following three kinds of graded Lie algebras in certain stable ranges: derivations of the free associative algebra, derivations of the free Lie algebra and symplectic derivations of the free associative algebra. In each case, we consider both the whole derivation Lie algebra and its ideal consisting of derivations with positive degrees. As an application of the last case, and by making use of a theorem of Kontsevich, we obtain a new proof of the vanishing theorem of Harer concerning the top rational cohomology group of the mapping class group with respect to its virtual cohomological dimension.

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“…Combining Hain's result above and the fact that Coker 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: Then Morita Showedmentioning

confidence: 99%

“…Except for these results, there are few results for the cokernels of the Johnson homomorphisms of the mapping class groups. Recently, based on a work of Hain [21], Naoya Enomoto and the author proved Theorem 1.2 (Enomoto and Satoh [17]). (= Theorem 8.7.)…”

mentioning

confidence: 99%