Work

The wheel classes in the locally finite homology of GLn(ℤ), canonical integrals and zeta values

Year: 2025

Type: article

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 nonzero classes in: the locally finite homology of the general linear group GL n .Z/ in both odd and even ranks, the homology of the moduli space of tropical curves, and the moduli space of tropical abelian varieties.We deduce the canonical integrals of a doubly infinite family of auxiliary classes in the even commutative graph complex.The proof also leads to a formula for the complete antisymmetrisation of a product of 2n 1 matrices of rank n, in the spirit of the Amitsur-Levitzki theorem.

Source: Geometry & Topology

DOI: 10.2140/gt.2025.29.4389

Authors: Francis Brown, Oliver Schnetz

Institutions: University of Oxford, Universität Hamburg

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: European Commission, Université de Genève, H2020 European Research Council

Awards: G434337789, Galois theory of periods and applications.