The adjoint Reidemeister torsion for the connected sum of knots

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-dime...

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Detalles Bibliográficos
Autores: Porti, Joan|||0000-0003-2554-3709, Yoon, Seokbeom
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:288310
Acceso en línea:https://ddd.uab.cat/record/288310
https://dx.doi.org/urn:doi:10.4171/QT/180
Access Level:acceso abierto
Palabra clave:Connected sum
Reidemeister torsion
Vanishing identity
Character variety
Descripción
Sumario: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.