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The Goldman-Turaev Lie bialgebra and the Johnson homomorphisms

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arxiv 1304.1885 v1 pith:7JLIVA4V submitted 2013-04-06 math.GT math.AGmath.AT

Nariya Kawazumi , Yusuke Kuno This is my paper · ORCID
classification math.GTmath.AGmath.AT
keywords bialgebragoldman-turaevhomomorphismsjohnsonapproachgeometricsurvey
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We survey a geometric approach to the Johnson homomorphisms using the Goldman-Turaev Lie bialgebra.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The formality of the Goldman-Turaev Lie bialgebra on a closed surface

    math.QA 2025-02 accept novelty 8.0 of 10

    The pro-unipotent automorphism group of the associated graded Goldman-Turaev Lie bialgebra on a closed surface is explicitly described in terms of a divergence map and the kernel of a reduced coproduct.

  2. A family of algebraic operations extending the Turaev cobracket

    math.QA 2025-02 accept novelty 7.0 of 10

    A new family of algebraic operations, the k-divergences, generalizes the Turaev cobracket and, for free associative algebras, coincides with ribbon graph operations and the standard cohomology generators of gl_n.

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