T. Willwacher

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20242026

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6 papers · 1 filter

math.QA2026

On free generators in the Grothendieck-Teichmüller Lie Algebra

Thomas Willwacher

We prove that any homogeneous family $σ_{3}, σ_{5}, \dots$ in $grt_{1} (K)$ with nonzero coefficients of $x^{2 k} y$ in $σ_{2 k + 1}$ generates a free Lie subalgebra, buildin…

math.QA2026

The Johnson homomorphism, embedding calculus and graph complexes

Florian Naef, Thomas Willwacher

We explain how the Johnson homomorphism and the Enomoto-Satoh trace, as well as higher-loop-order generalizations, can be obtained from graph complexes originating in the Goodwilli…

math.QA2025

Real models for the framed little $n$ -disks operads

Anton Khoroshkin, Thomas Willwacher

We study the action of the orthogonal group on the little $n$ -disks operads. As an application we provide small models (over the reals) for the framed little $n$ -disks operads. It…

math.QA2025

Numerical computation of linearized KV and the Deligne-Drinfeld and Broadhurst-Kreimer conjectures

Florian Naef, Thomas Willwacher

We compute numerically the dimensions of the graded quotients of the linearized Kashiwara-Vergne Lie algebra lkv in low weight, confirming a conjecture of Raphael-Schneps in those…

math.QA2024

The oriented graph complex revisited

Sergei Merkulov, Thomas Willwacher, Vincent Wolff

We prove that the Kontsevich graph complex $G C_{d}^{2}$ and its oriented version $O G C_{d + 1}^{2}$ are quasi-isomorphic as dg Lie algebras.

math.QA2024

Weight 2 cohomology of graph complexes of cyclic operads and the handlebody group

Michael Borinsky, Benjamin BrÃ¼ck, Thomas Willwacher

We compute the weight 2 cohomology of the Feynman transforms of the cyclic (co)operads $BV$ and $HyCom$ , and the top $- 2$ weight cohomology of the Feynman transfor…