## Algebraic & Geometric Topology

### The profinite completions of knot groups determine the Alexander polynomials

Jun Ueki

#### Abstract

We study several properties of the completed group ring $ℤ ̂ [ [ t ℤ ̂ ] ]$ 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 18, Number 5 (2018), 3013-3030.

Dates
Revised: 21 February 2018
Accepted: 5 March 2018
First available in Project Euclid: 30 August 2018

https://projecteuclid.org/euclid.agt/1535594429

Digital Object Identifier
doi:10.2140/agt.2018.18.3013

Mathematical Reviews number (MathSciNet)
MR3848406

Zentralblatt MATH identifier
06935827

#### Citation

Ueki, Jun. The profinite completions of knot groups determine the Alexander polynomials. Algebr. Geom. Topol. 18 (2018), no. 5, 3013--3030. doi:10.2140/agt.2018.18.3013. https://projecteuclid.org/euclid.agt/1535594429

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