The adjoint Reidemeister torsion for the connected sum of knots

Joan Porti, Seokbeom Yoon

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Abstract

Let K be the connected sum of knots K1​,…,Kn​. It is known that the SL2​(C)-character variety of the knot exterior of K has a component of dimension ≥2 as the connected sum admits a so-called bending. We show that there is a natural way to define the adjoint Reidemeister torsion for such a high-dimensional component and prove that it is locally constant on a subset of the character variety where the trace of a meridian is constant. We also prove that the adjoint Reidemeister torsion of K satisfies the vanishing identity if each Ki​ does so.
Original languageEnglish
Pages (from-to)407-428
Number of pages22
JournalQuantum Topology
Volume14
Issue number3
DOIs
Publication statusPublished - 16 Sept 2023

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