### M Theory Lesson 187

Bar-Natan describes the correspondence between chords and self intersections in knots. A crossing of chords becomes a crossing in the knot diagram. This work led to the classic paper [1], which in turn was used by Broadhurst and Kreimer [2] to analyse the algebra of MZVs as it appears in QFT, although the latter paper uses chorded braid diagrams to represent zeta values. Nowadays we understand that the MZV algebra comes from motivic integrals on spaces tiled by the associahedra, so we expect associahedra and chorded braids to be closely linked.

[1] T.Q.T. Le and J. Murakami, Topology and Appl. 62 (1995) 193-206

[2] D.J. Broadhurst and D. Kreimer, Physics Lett. B 393 (1997) 403-412

[1] T.Q.T. Le and J. Murakami, Topology and Appl. 62 (1995) 193-206

[2] D.J. Broadhurst and D. Kreimer, Physics Lett. B 393 (1997) 403-412

## 2 Comments:

Okay, wouldn't the diagram at the top right look more like an "8" instead of an "X"?

Oh, sure, but I was too lazy to draw it all in. Sorry! I have recommended the Broadhurst/Kreimer paper many times before. You simply must read it.

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