Premium
Coloured Jones invariants of links and the Volume Conjecture
Author(s) -
Costantino Francesco
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm029
Subject(s) - conjecture , extension (predicate logic) , mathematics , combinatorics , volume (thermodynamics) , state (computer science) , pure mathematics , discrete mathematics , computer science , physics , algorithm , quantum mechanics , programming language
Abstract We extend the definition of the coloured Jones polynomials to framed links and trivalent graphs in S 3 # k (S 2 × S 1 ) using a state‐sum formulation based on Turaev's shadows. Then, we prove that the natural extension of the Volume Conjecture holds true for an infinite family of hyperbolic links.