nLab
trace of horizontal to round chord diagrams

Contents

Contents

Idea

In knot theory, a certain trace-like operation turns horizontal chord diagrams into round chord diagrams:

Given a horizontal chord diagram on nn strands and given any choice of cyclic permutation of nn elements, the trace is the round chord diagram obtained by gluing the ends of the strands according to the cyclic permutation, and retaining the chords in the evident way.

The following graphics shows basic examples of the trace operation for cyclic permutation of strands one step to the right:

Properties

Relation to 4T relations

The trace operation sends the 4T relations on horizontal chord diagrams to those for round chord diagrams:

References

The trace operation is implicit in

It is made a little more explicit in

Created on November 28, 2019 at 02:47:05. See the history of this page for a list of all contributions to it.