Guts determine the leading coefficients of $L^2$-Alexander torsions
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- by Jianru Duan;
- Trans. Amer. Math. Soc. 378 (2025), 3699-3720
- DOI: https://doi.org/10.1090/tran/9384
- Published electronically: March 5, 2025
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Abstract:
For 3-manifolds, the leading coefficient of the $L^2$-Alexander torsion is a numerical invariant of a real first cohomology class. We show that the leading coefficient equals the relative $L^2$-torsion of the manifold cut up along a norm-minimizing surface dual to the cohomology class. Furthermore, the leading coefficient equals the relative $L^2$-torsion of the guts associated to the cohomology class. Finally, we prove that the leading coefficient is constant on any open Thurston cone. The main ingredients are a new criterion for the convergence of Fuglede–Kadison determinants and the work of Agol and Zhang on guts of 3-manifolds.References
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Bibliographic Information
- Jianru Duan
- Affiliation: Beijing International Center for Mathematical Research, No. 5 Yiheyuan Road, Haidian District, Beijing 100871, People’s Republic of China
- MR Author ID: 1623618
- Email: duanjr@stu.pku.edu.cn
- Received by editor(s): December 12, 2023
- Received by editor(s) in revised form: July 18, 2024, and November 26, 2024
- Published electronically: March 5, 2025
- © Copyright 2025 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 378 (2025), 3699-3720
- MSC (2020): Primary 57K31; Secondary 57Q10
- DOI: https://doi.org/10.1090/tran/9384