The wheel classes in the locally finite homology of $\mathrm{GL}_n(\mathbb{Z})$, canonical integrals and zeta values
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908688318464000 |
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| author | Brown, Francis Schnetz, Oliver |
| author_facet | Brown, Francis Schnetz, Oliver |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The wheel classes in the locally finite homology of $\mathrm{GL}_n(\mathbb{Z})$, canonical integrals and zeta values Brown, Francis Schnetz, Oliver Number Theory Mathematical Physics K-Theory and Homology 20J06, 11H55, 11F75, 11F06, 14T20, 18G85, 11M32, 81Q30 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. |
| title | The wheel classes in the locally finite homology of $\mathrm{GL}_n(\mathbb{Z})$, canonical integrals and zeta values |
| topic | Number Theory Mathematical Physics K-Theory and Homology 20J06, 11H55, 11F75, 11F06, 14T20, 18G85, 11M32, 81Q30 |
| url | https://arxiv.org/abs/2402.06757 |