Geometry of knots and links
type: Item
instance of: scholarly article
title: Geometry of knots and links
zbMATH Open document ID: 1478.57002
DOI: 10.4171/IRMA/33-1/20
publication date: 2021-12-03T00:00:00Z
review text: Summary: We give an overview of recent results on the geometry of knots and links. More precisely, we investigate the existence of hyperbolic, spherical or Euclidean structure on various cone manifolds whose underlying space is the three-dimensional sphere and whose singular set is a given knot or link. We present trigonometrical identities involving the lengths of singular geodesics and cone angles of such cone manifolds. Then these identities are used to produce exact integral formulas for volumes of the corresponding cone manifolds. For the entire collection see [Zbl 1466.57001].
Mathematics Subject Classification ID: 57K10
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 51M25
Mathematics Subject Classification ID: 57-02
zbMATH DE Number: 7438874
zbMATH Keywords: geometry of knots and links
zbMATH Keywords: hyperbolic
zbMATH Keywords: spherical
zbMATH Keywords: Euclidean
zbMATH Keywords: cone-manifold
zbMATH Keywords: singular set
zbMATH Keywords: trigonometrical identities
zbMATH Keywords: cone angles
zbMATH Keywords: volume
author: Nikolaĭ Vladimirovich Abrosimov
author: Alexander Mednykh
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 7438874