Abstract
Let L = ℓ1 ∪⋯∪ℓd+1 be an oriented link in 𝕊3, and let L(q) be the d-component link ℓ1 ∪⋯∪ℓd regarded in the homology 3-sphere that results from performing 1/q-surgery on ℓd+1. Results about the Alexander polynomial and twisted Alexander polynomials of L(q) corresponding to finite-image representations are obtained. The behavior of the invariants as q increases without bound is described.
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