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TWISTED ALEXANDER INVARIANTS OF TWISTED LINKS

DANIEL S. SILVER

Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA

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and

SUSAN G. WILLIAMS

Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA

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https://doi.org/10.1142/S0218216512501180Cited by:1 (Source: Crossref)

Abstract

Let L = ℓ₁ ∪⋯∪ℓ_d+1 be an oriented link in 𝕊³, and let L(q) be the d-component link ℓ₁ ∪⋯∪ℓ_d regarded in the homology 3-sphere that results from performing 1/q-surgery on ℓ_d+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.

Keywords:

AMSC: 57M25, 37B10, 37B40

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