Quantum Topology


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Volume 8, Issue 2, 2017, pp. 295–360
DOI: 10.4171/QT/91

Published online: 2017-05-29

Galois action on knots I: Action of the absolute Galois group

Hidekazu Furusho[1]

(1) Nagoya University, Japan

Our aim of this and subsequent papers is to enlighten (a part of, presumably) arithmetic structures of knots. This paper introduces a notion of profinite knots which extends topological knots and shows its various basic properties. Particularly an action of the absolute Galois group of the rational number field on profinite knotsis rigorously established, which is attained by our extending the action of Drinfeld's Grothendieck–Teichmüller group on profinite braid groups into on profinite knots.

Keywords: Profinite knots, absolute Galois group, Grothendieck–Teichmüller group

Furusho Hidekazu: Galois action on knots I: Action of the absolute Galois group. Quantum Topol. 8 (2017), 295-360. doi: 10.4171/QT/91