Geodesic
The profinite completions of knot groups determine the Alexander polynomials
Ueki, Jun1
1 Department of Mathematics, School of System Design and Technology, Tokyo Denki University, Tokyo, Japan
Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 3013-3030

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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

DOI : 10.2140/agt.2018.18.3013
Classification : 57M27, 20E18, 20E26, 57M12
Keywords: profinite completion, profinite group ring, knot, branched covering

Ueki, Jun 1

1 Department of Mathematics, School of System Design and Technology, Tokyo Denki University, Tokyo, Japan 
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Ueki, Jun. The profinite completions of knot groups determine the Alexander polynomials. Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 3013-3030. doi: 10.2140/agt.2018.18.3013

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