User:Drorbn/06-1350-HW4

The Generators

Our generators are $T$, $R$, $Y=\Phi$ and $B^{\pm}$ (we might consider splitting $Y$ into two, $Y^{up}$ and $Y^{dn}$):

Picture
Generator	$T$	$R$	$Y^{up}$	$Y^{dn}$	$B^+$	$B^-$
Perturbation	$t$	$r$	$y^u$	$y^d$	$b^+$	$b^-$

The Relations

The Reidemeister Move R3

The picture is

In formulas, this is

$(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ = (1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+$.

Thus the R3 component of $d$ is

$(1230)^\star b^+ +(1213)^\star b^+ +(1023)^\star b^+ -(1123)^\star b^+ -(1203)^\star b^+ -(1231)^\star b^+$.