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- W2168764676 abstract "For a knot K in a homology 3-sphere Σ, by Σ( K;p/q ), we denote the resulting 3-manifold of p/q -surgery along K . We say that the manifold or the surgery is of lens type if Σ( K;p/q ) has the same Reidemeister torsion as a lens space. We prove that, for Σ( K;p/q ) to be of lens type, it is a necessary and sufficient condition that the Alexander polynomial Δ K (t) of K is equal to that of an ( i, j )-torus knot T(i, j) modulo ( t p – 1). We also deduce two results: If Σ( K;p/q ) has the same Reidemeister torsion as L(p, q') then (1) (2) The multiple of Σ K ( t k ) over k ∈ ( i ) is ± t m modulo ( t p – 1), where ( i ) is the subgroup in ( Z/ p Z ) × /{±1} generated by i . Conversely, if a subgroup H of ( Z/ p Z ) × /{±l} satisfying that the product of Σ K ( t k ) ( k ∈ H ) is ± t m modulo ( t p – 1), then H includes i or j . Here, i, j are the parameters of the torus knot above." @default.
- W2168764676 created "2016-06-24" @default.
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- W2168764676 date "2007-02-01" @default.
- W2168764676 modified "2023-09-26" @default.
- W2168764676 title "A deformation of the Alexander polynomials of knots yielding lens spaces" @default.
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- W2168764676 doi "https://doi.org/10.1017/s0004972700038995" @default.
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