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2021 Infinitesimal gluing equations and the adjoint hyperbolic Reidemeister torsion
Rafał Siejakowski
Tohoku Math. J. (2) 73(4): 597-626 (2021). DOI: 10.2748/tmj.20200828

Abstract

We establish a link between the derivatives of Thurston's hyperbolic gluing equations on an ideally triangulated finite volume hyperbolic 3-manifold and the cohomology of the sheaf of infinitesimal isometries. This provides a geometric reformulation of the non-abelian Reidemeister torsion corresponding to the adjoint of the monodromy representation of the hyperbolic structure. These results are then applied to the study of the `1-loop Conjecture' of Dimofte--Garoufalidis, which we generalize to arbitrary 1-cusped hyperbolic 3-manifolds. We verify the generalized conjecture in the case of the sister manifold of the figure-eight knot complement.

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Rafał Siejakowski. "Infinitesimal gluing equations and the adjoint hyperbolic Reidemeister torsion." Tohoku Math. J. (2) 73 (4) 597 - 626, 2021. https://doi.org/10.2748/tmj.20200828

Information

Published: 2021
First available in Project Euclid: 22 December 2021

Digital Object Identifier: 10.2748/tmj.20200828

Subjects:
Primary: 57Q10
Secondary: 57M50

Keywords: gluing equations , hyperbolic 3-manifolds , ideal triangulations , Reidemeister torsion

Rights: Copyright © 2021 Tohoku University

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Vol.73 • No. 4 • 2021
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