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- W2951367322 abstract "The Jones polynomial of a knot in 3-space is a Laurent polynomial in $q$, with integer coefficients. Many people have pondered why is this so, and what is a proper generalization of the Jones polynomial for knots in other closed 3-manifolds. Our paper centers around this question. After reviewing several existing definitions of the Jones polynomial, we show that the Jones polynomial is really an analytic function, in the sense of Habiro. Using this, we extend the holonomicity properties of the colored Jones function of a knot in 3-space to the case of a knot in an integer homology sphere, and we formulate an analogue of the AJ Conjecture. Our main tools are various integrality properties of topological quantum field theory invariants of links in 3-manifolds, manifested in Habiro's work on the colored Jones function.Revised version updating references on Witten-Reshetikhin-Turaev invariants." @default.
- W2951367322 created "2019-06-27" @default.
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- W2951367322 date "2006-01-07" @default.
- W2951367322 modified "2023-09-27" @default.
- W2951367322 title "Is the Jones polynomial of a knot really a polynomial" @default.
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