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2018 The profinite completions of knot groups determine the Alexander polynomials
Jun Ueki
Algebr. Geom. Topol. 18(5): 3013-3030 (2018). DOI: 10.2140/agt.2018.18.3013

Abstract

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 Δ J ( t ) and Δ K ( t ) coincide.

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Jun Ueki. "The profinite completions of knot groups determine the Alexander polynomials." Algebr. Geom. Topol. 18 (5) 3013 - 3030, 2018. https://doi.org/10.2140/agt.2018.18.3013

Information

Received: 24 September 2017; Revised: 21 February 2018; Accepted: 5 March 2018; Published: 2018
First available in Project Euclid: 30 August 2018

zbMATH: 06935827
MathSciNet: MR3848406
Digital Object Identifier: 10.2140/agt.2018.18.3013

Subjects:
Primary: 57M27
Secondary: 20E18, 20E26, 57M12

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 5 • 2018
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