On the conjecture of the Galois invariance of the Tutte polynomial for Grothendieck's dessins d'enfants

N. Amburg^abc, L. Bril<sup>b

a</sup> National Research Centre "Kurchatov Institute", Moscow
^b National Research University Higher School of Economics, Moscow
^c Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: Yuri Manin and Matilde Marcolli proposed a novel method of constructing invariants of the action of the absolute Galois group on Grothendieck's dessins d'enfant. In particular, they formulated the conjecture that the Tutte polynomial is an example of such an invariant. In this note, we present a counterexample that refutes this conjecture.

UDC: 511.238