Theory Update 38

In Khovanov homology the bit values, $0$ and $1$, are associated to smoothings of a knot crossing. The trefoil knot in the braid group $B_2$ has three crossings. Let us label these three bits $X$, $Y$ and $Z$. A Bilson-Thompson particle braid is an element of the braid group $B_3$, although its ribbon strands may be either twisted or untwisted. Two crossings on a ribbon strand represent a $1/3$ down quark charge.