Volume 18, issue 5 (2018)

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The profinite completions of knot groups determine the Alexander polynomials

Jun Ueki

Algebraic & Geometric Topology 18 (2018) 3013–3030

We study several properties of the completed group ring ̂[[t ̂]] and the completed Alexander modules of knots. Then we prove that if the profinite completions of the groups of two knots J and K are isomorphic, then their Alexander polynomials ΔJ(t) and ΔK(t) coincide.

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profinite completion, profinite group ring, knot, branched covering
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 20E18, 20E26, 57M12
Received: 24 September 2017
Revised: 21 February 2018
Accepted: 5 March 2018
Published: 22 August 2018
Jun Ueki
Department of Mathematics
School of System Design and Technology
Tokyo Denki University