Journal article
The wheel classes in the locally finite homology of GLn(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 GLn(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 anti-symmetrisation of a product of 2n − 1 matrices of rank n, in the spirit of the Amitsur-Levitzki theorem.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 955.0KB, Terms of use)
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- Publisher copy:
- 10.2140/gt.2025.29.4389
Authors
- Publisher:
- Mathematical Sciences Publishers
- Journal:
- Geometry and Topology More from this journal
- Volume:
- 29
- Issue:
- 8
- Pages:
- 4389-4447
- Publication date:
- 2025-11-26
- Acceptance date:
- 2025-03-14
- DOI:
- EISSN:
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1364-0380
- ISSN:
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1465-3060
- Language:
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English
- Keywords:
- Pubs id:
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2100683
- Local pid:
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pubs:2100683
- Deposit date:
-
2025-03-27
Terms of use
- Copyright holder:
- Brown and Schnetz
- Copyright date:
- 2025
- Rights statement:
- © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).
- Licence:
- CC Attribution (CC BY)
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