A regular homotopy version of the Goldman-Turaev Lie bialgebra, the Enomoto-Satoh traces and the divergence cocycle in the Kashiwara-Vergne problem

Abstract

By introducing a refinement of the Goldman-Turaev Lie bialgebra, we interpret the divergence cocycle in the Kashiwara-Vergne problem and the Enomoto-Satoh obstructions for the surjectivity of the Johnson homomorphisms as some part of a regular homotopy version of the Turaev cobracket.

arXiv commentAn announcement on the author's research in progress. Submitted to Sūrikaisekikenkyūsho Kōkyūroku (RIMS, Kyoto University, Japan)

References in corpus (2)

• Groupoid-theoretical methods in the mapping class groups of surfaces
• Intersections of curves on surfaces and their applications to mapping class groups

Cited by in corpus (3)

• Poisson algebras of curves on bordered surfaces and skein quantization
• A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces
• A tensorial description of the Turaev cobracket on genus 0 compact surfaces