Galois action on knots II: Proalgebraic string links and knots

2014/05/19 by Furusho, Hidekazu · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1405.4575

Abstract

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.

Cited by

• The Kontsevich invariant and the action of the Grothendieck--Teichmüller group on 2-component string links

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