On the positivity of twisted L2–torsion for 3–manifolds

Duan, Jianru

doi:10.2140/agt.2024.24.2307

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On the positivity of twisted $L^2$–torsion for $3$–manifolds

Jianru Duan

Algebraic & Geometric Topology 24 (2024) 2307–2329

DOI: 10.2140/agt.2024.24.2307

Abstract

For any compact orientable irreducible $3$ –manifold $N$ with empty or incompressible toral boundary, the twisted $L^{2}$ –torsion is a nonnegative function defined on the representation variety $Hom (π_{1} (N), SL (n, ℂ))$ . We show that if $N$ has infinite fundamental group, then the $L^{2}$ –torsion function is strictly positive. Moreover, this torsion function is continuous when restricted to the subvariety of upper triangular representations.

Keywords

$3$–manifolds, twisted $L^2$–torsion

Mathematical Subject Classification

Primary: 57K31

References

Publication

Received: 27 October 2022

Revised: 3 January 2023

Accepted: 13 March 2023

Published: 16 July 2024

Authors

Jianru Duan
Beijing International Center for Mathematical Research Peking University Beijing China

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Volume 24, issue 4 (2024)