Abstract
In this paper we define the Reidemeister torsion as a rational function on the geometric components of the character variety of a one-cusped hyperbolic manifold $M$. We study its poles and zeros, and we deduce sufficient conditions on the manifold $M$ for this function being non-constant.
Acknowledgments
This work is part of the author's PhD dissertation, which has been conducted in Sorbonne-Université, Institut de Mathématiques de Jussieu - Paris Rive Gauche. The author has benefited of a constant support from his advisor Julien Marché, and thanks him for his time and help. He thanks Teruaki Kitano and Joan Porti for having suggested to study the acyclic torsion, and for sharing with him helpful advices on the topic. Finally, we thank the anonymous referees for their numerous remarks and comments that have contributed to improve the writing of the paper. In particular, comments of an anonymous referee on a previous version of this manuscript have led to a complete rewriting of Lemma 2.18 and of Subsection 5.2. We thank him/her for that.
Citation
Leo Benard. "Torsion function on character varieties." Osaka J. Math. 58 (2) 291 - 318, April 2021.
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