Detecting the orientation of long links by finite type invariants

2005/07/01 by Duzhin, S. V., Karev, M. V.
#Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.math/0507015

Abstract

We prove the existence of a degree 7 Vassiliev invariant of long (or string) two-component links which is not preserved under the simultaneous change of orientation of both components. The non-invertibility of this invariant can be detected by the standard weight system with values in the tensor square of the universal enveloping algebra for \gl(n).

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