Symmetric links and Conway sums: volume and Jones polynomial

Abstract

We obtain bounds on hyperbolic volume for periodic links and Conway sums of alternating tangles. For links that are Conway sums we also bound the hyperbolic volume in terms of the coefficients of the Jones polynomial.

18 pages, 7 figures. Revised according to referee's comments. To appear in Mathematical Research Letters.

References in corpus (5)

• Ricci Flow and the Poincare Conjecture
• The Jones polynomial and graphs on surfaces
• The minimal volume orientable hyperbolic 2-cusped 3-manifolds
• Minimum-volume hyperbolic 3-manifolds
• Cusp areas of Farey manifolds and applications to knot theory

Cited by in corpus (19)

• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• Slopes and colored Jones polynomials of adequate knots
• Alternating sum formulae for the determinant and other link invariants
• Cusp areas of Farey manifolds and applications to knot theory
• Separability and the genus of a partial dual
• Volume bounds for generalized twisted torus links
• Partial duals of plane graphs, separability and the graphs of knots
• On the Seifert graphs of a link diagram and its parallels
• On diagrammatic bounds of knot volumes and spectral invariants
• Alternating links on surfaces and volume bounds
• The lowest volume 3-orbifolds with high torsion
• Jones polynomials, volume, and essential knot surfaces: a survey
• Density spectra for knots
• Excluded minors and the ribbon graphs of knots
• Cusp Volumes of Alternating Knots on Surfaces
• Volume and geometry of homogeneously adequate knots
• Linear Bounds of the Crosscap Number of Knots
• Combinatorics of Link Diagrams and Volume
• Waist size for cusps in hyperbolic 3-manifolds II