Ko Honda’s Octahedral Relation

This morning at Kirbyfest (Happy Birthday!) Ko Honda gave a talk about his work on developing a contact category. You’ve got an oriented surface (with boundary) together with dividing curves as your objects. Morphisms arise via bypass moves. Ko noticed that the octahedral relation is satisfied:

Ko's Octahedral relation-2

We see four arcs of the Red dividing curves in a White disk of the surface.

The Green triangles are the exact triangles. The Yellow triangles are the commuting triangles.

Ko's Octahedral relation-3

Ko's Octahedral relation-4

Ko's Octahedral relation-1

You can get the SketchUp model here. The disks remain facing the camera in the horizontal direction by using the “face me” function of a component.

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~ by Ken Baker on August 13, 2008.

One Response to “Ko Honda’s Octahedral Relation”

  1. Honda informs me that it is usually called The Octahedral Axiom.

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