Categorifying Coloring Numbers

Details Categorifying Coloring Numbers Categorifying Coloring Numbers

2008-03-11

arxiv.org/abs/0803.1642v1

Mathematics

Geometric Topology

To appear in "Interactions between Representation Theory, Quantum Field Theory, Category Theory, and Quantum Information Theor

Scientific paper

Coloring numbers are one of the simplest combinatorial invariants of knots and links to describe. And with Joyce's introduction of quandles, we can understand them more algebraically. But can we extend these invariants to tangles -- knots and links with free ends? Indeed we can, once we categorify. Starting from the definition of coloring numbers, we will categorify them and establish this extension to tangles. Then, decategorifying will leave us with matrix representations of the monoidal category of tangles.

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