A Survey of the Impact of Thurston’s Work on Knot Theory

Sakuma, Masashi

doi:10.1007/978-3-030-55928-1_3

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2022

2023

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Cited by 2 publications

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“…We review basic notions on knots in accordance with [29]. A knot 𝐾 is a smoothly embedded circle in the 3-sphere 𝑆 3 .…”

Section: Basic Notionsmentioning

confidence: 99%

Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds

Goda,

Morifuji

2023

Annales Mathématiques Blaise Pascal

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In this paper, we discuss a relationship between the chirality of knots and higher-dimensional twisted Alexander polynomials associated with holonomy representations of hyperbolic 3-cone-manifolds. In particular, we provide a new necessary condition for a knot, that appears in a hyperbolic 3-cone-manifold of finite volume as a singular set, to be amphicheiral. Moreover, we can detect the chirality of hyperbolic twist knots, according to our criterion, using low-dimensional irreducible representations.

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“…We review basic notions on knots in accordance with [29]. A knot 𝐾 is a smoothly embedded circle in the 3-sphere 𝑆 3 .…”

Section: Basic Notionsmentioning

confidence: 99%