The 1-Dimensional Tangle Hypothesis

I’ll discuss the 1-dimensional tangle hypothesis, which is a classification of certain link-invariants in terms of category theory.  The main idea is that a link can be chopped up into basic pieces.  Except for some `infinite homotopy types’, the moduli space of these basic pieces is combinatorial, and categorical in nature.  These infinite homotopy types can be accounted for by constructing an action of the orthogonal group, O(3), on braided-monoidal categories with duals, which will be the focus of this talk.  I hope this talk is accessible to any early-career graduate student!

 

This is joint work with John Francis.