The wheel classes in the locally finite homology of $\mathrm{GL}_n(\mathbb{Z})$, canonical integrals and zeta values

Abstract: We compute the canonical integrals associated to wheel graphs, and prove that they are proportional to odd zeta values. From this we deduce that wheel classes define explicit non-zero classes in: the locally finite homology of the general linear group $\GL_n(\ZZ)$ in both odd and even ranks, the homology of the moduli spaces of tropical curves, and the moduli space of tropical abelian varieties. We deduce the existence of a doubly infinite family of auxiliary classes in the even commutative graph complex.