2015
DOI: 10.2140/agt.2015.15.801
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The Johnson cokernel and the Enomoto–Satoh invariant

Abstract: 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 … Show more

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Cited by 13 publications
(39 citation statements)
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“…In [5] a "trace" map Tr C : D + → ⊕ n≥1 Ω n (V) was constructed. The spaces Ω n (V) are generated by graphs formed by adding n "external" oriented edges to a labeled tree from D + , while the trace map is defined by adding sets of edges to a tree in all possible ways, multiplying by contractions of labeling coefficients.…”
Section: Introductionmentioning
confidence: 99%
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“…In [5] a "trace" map Tr C : D + → ⊕ n≥1 Ω n (V) was constructed. The spaces Ω n (V) are generated by graphs formed by adding n "external" oriented edges to a labeled tree from D + , while the trace map is defined by adding sets of edges to a tree in all possible ways, multiplying by contractions of labeling coefficients.…”
Section: Introductionmentioning
confidence: 99%
“…In fact one recovers the abelianization obstructions from Theorem 1.1 by applying the map T(V) → Sym(V) to the coefficient modules. In obstruction modules from [5]:…”
Section: Introductionmentioning
confidence: 99%
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“…a 3 , a 4 , a 5 , b 2 , b 5 , b 3 , a 6 , a 7 , b 4 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 2 , a 6 , b3 , b 5 , b 6 , b 4 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 2 , a 6 , b 3 , b 5 , a 7 , b 4 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 2 , a 6 , b 3 , b 6 , b 5 , b 4 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 2 , a 6 , b 3 , a 7 , b 5 , b 4 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 2 , a 6 , b 3 , a 7 , b 5 , b 6 , b 4 , b 7 },{a 2 , a 3 , a 4 , a 5 , b 2 , b 4 , a 6 , b 3 , b 6 , b 5 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 2 , b 4 , a 6 , b 3 , a 7 , b 5 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 2 , a 6 , b 4 , b 3 , b 6 , b 5 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 2 , a 6 , b 4 , b 3 , a 7 , b 5 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 2 , a 6 , b 6 , b 3 , b 4 , b 5 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 2 , a 6 , a 7 , b 3 , b 4 , b 5 , b 6 , b 7 },…”
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“…a 3 , a 4 , a 5 , b 3 , b 2 , b 4 , a 6 , b 6 , b 5 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 3 , b 2 , b 4 , a 6 , a 7 , b 5 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b3 , b 2 , a 6 , b 4 , b 6 , b 5 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 3 , b 2 , a 6 , b 4 , a 7 , b 5 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 3 , b 2 , a 6 , a 7 , b 4 , b 5 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 3 , b 2 , a 6 , a 7 , b 4 , b 6 , b 5 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 3 , b 2 , b 5 , a 6 , b 6 , b 4 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 3 , b 2 , b 5 , a 6 , a 7 , b 4 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 3 , b 2 , a 6 , b 5 , b 6 , b 4 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 3 , b 2 , a 6 , b 5 , a 7 , b 4 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 4 , b 2 , b 3 , a 6 , b 6 , b 5 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 4 , b 2 , b 3 , a 6 , a 7 , b 5 , b 6 , b 7 },{a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 3 , b 4 , b 6 , b 5 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 3 , b 4 , a 7 , b 5 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 3 , b 5 , b 4 , b 6 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 3 , b 6 , b 4 , b 5 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 3 , a 7 , b 4 , b 5 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 3 , a 7 , b 4 , b 6 , b 5 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 5 , b 2 , b 3 , a 6 , a 7 , b 4 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 3 , b 5 , b 6 , b 4 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 3 , b 5 , a 7 , b 4 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 3 , b 6 , b 5 , b 4 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 3 , a 7 , b 5 , b 4 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 3 , a 7 , b 5 , b 6 , b 4 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 4 , b 2 , a 6 , b 3 , b 6 , b 5 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , b 4 , b 2 , a 6 , b 3 , a 7 , b 5 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 4 , b 3 , b 6 , b 5 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 4 , b 3 , a 7 , b 5 , b 6 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , b 6 , b 3 , b 4 , b 5 , a 7 , b 7 }, {a 2 , a 3 , a 4 , a 5 , a 6 , b 2 , a 7 , b 3 , b 4 , b 5 , b 6 , b 7 },…”
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