A tensorial description of the Turaev cobracket on genus 0 compact surfaces

TL;DR

This paper provides a tensorial framework for understanding the Turaev cobracket on genus 0 compact surfaces, utilizing standard group-like expansions and highlighting the role of Bernoulli numbers.

Contribution

It introduces a novel tensorial description of the Turaev cobracket specifically for genus 0 surfaces, connecting algebraic structures with classical number theory.

Findings

Tensorial description of Turaev cobracket established

Bernoulli numbers appear in the tensorial framework

Enhanced understanding of surface topology and algebraic structures

Abstract

We give a tensorial description of the Turaev cobracket on any genus 0 compact surface through the standard group-like expansion, where the Bernoulli numbers appear.