Australian Category Seminar

Expansion Categories and Goldman-Turaev Formality

Joel Richardson·28 October 2026

We recently heard from Zsuzsanna Dancso about constructing expansions of the Goldman-Turaev Lie bialgebra from the Kontsevich integral. In this talk, we’ll realise this construction within a larger categorical framework. We’ll discuss idempotent endofunctors and their associated expansion categories, as well as algebraic objects (i.e. monoid objects, Lie algebra objects, etc) therein. We’ll show that morphisms of idempotent endofunctors induce functors between expansion categories, and use this, together with pullbacks and pushouts, to turn the Kontsevich integral (an expansion of the braid group) into an expansion of the Goldman-Turaev Lie bialgebra.

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