The profinite completions of knot groups determine the Alexander polynomials

Jun Ueki

doi:10.2140/agt.2018.18.3013

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arXiv · 1702.03836

The profinite completions of knot groups determine the Alexander polynomials

Jun Ueki

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Abstract

We study several properties of the completed group ring $\widehat{\mathbb{Z}}[[t^{\widehat{\mathbb{Z}}}]]$ 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 $\Delta_J(t)$ and $\Delta_K(t)$ coincide.

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Jun Ueki. 2017-02-13. The profinite completions of knot groups determine the Alexander polynomials. https://doi.org/10.2140/agt.2018.18.3013

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