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...
| Autores: | , |
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| 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 |
| 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. |
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