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Bibliographic Details
Main Authors: Bar-Natan, Dror, Dancso, Zsuzsanna, Hogan, Tamara, Liu, Jessica, Scherich, Nancy
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.20983
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Table of Contents:
  • We present a new solution to the formality problem for the framed Goldman--Turaev Lie bialgebra, constructing Goldman-Turaev homomorphic expansions (formality isomorphisms) from the Kontsevich integral. Our proof uses a three dimensional derivation of the Goldman-Turaev Lie biaglebra arising from a low-degree Vassiliev quotient -- the {\em emergent} quotient -- of tangles in a thickened punctured disk, modulo a Conway skein relation. This is in contrast to Massuyeau's 2018 proof using braids. A feature of our approach is a general conceptual framework which is applied to prove the compatibility of the homomorphic expansion with both the Goldman bracket and the technically challenging Turaev cobracket.