Galois Action on Knots II: Proalgebraic String Links and Knots

  • Hidekazu FurushoEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 314)


We discuss an action of the Grothendieck-Teichmüller proalgebraic group on the linear span of proalgebraic tangles, oriented tangles completed by a filtration of Vassiliev. The action yields a motivic structure on tangles. We derive distinguished properties of the action particularly on proalgebraic string links and on proalgebraic knots which can not be observed in the action on proalgebraic braids. By exploiting the properties, we explicitly calculate the inverse image of the trivial (the chordless) chord diagram under the Kontsevich isomorphism.


Proalgebraic tangles Chord diagrams Grothendieck-Teichmüller group Associators 



Part of the paper was written at Max Planck Institute for Mathematics. The author also thanks the institute for its hospitality. The referees’ efforts to make this paper better is gratefully acknowledged. This work was supported by Grant-in-Aid for Young Scientists (A) 24684001.


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Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityFuro-choJapan

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