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.

Final version. Corrected typos and expanded some parts of the introduction following referee's suggestions. Attached file `CanonicalIntegrals' contains Maple code to compute the canonical integrals in the paper using HyperlogProcedures

References in corpus (2)

• Tropical Monte Carlo quadrature for Feynman integrals
• Invariant Differential Forms on Complexes of Graphs and Feynman Integrals

Cited by in corpus (1)

• Unstable cohomology of ${\mathsf{GL}}_{2n}(\mathbb{Z})$ and the odd commutative graph complex