Pensieve header: Verifying the genus conjecture.

Loading the genus data obtained from https://knotinfo.org/:

SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\Theta"];

<<Theta.m

GenusData=Cases[
Import["C:\\drorbn\\AcademicPensieve\\Projects\\Theta\\GenusInfoFromKnotInfo.org.csv"][[2;;]],
{K_,g_}:>(KnotGenus[Evaluate[Knot@K]]=ToExpression@g),
∞];
KnotGenus[Knot[8,17]]

FiberedKnots=Cases[
Import["C:\\drorbn\\AcademicPensieve\\Projects\\Theta\\FiberedInfoFromKnotInfo.org.csv"],
{K_,"Y"}:>Knot@K,
∞]

Ribbons={Knot[0,1],Knot[6,1],Knot[8,8],Knot[8,9],Knot[8,20],Knot[9,27],Knot[9,41],Knot[9,46],Knot[10,3],Knot[10,22],Knot[10,35],Knot[10,42],Knot[10,48],Knot[10,75],Knot[10,87],Knot[10,99],Knot[10,123],Knot[10,129],Knot[10,137],Knot[10,140],Knot[10,153],Knot[10,155]}

DeltaTable=Table[K->Θ[K][[1]], {K,AllKnots[{3,10}]}]

ThetaTable=Table[K->(Θ[K][[2]]/.{(Subscript[T, 1])->T, (Subscript[T, 2])->S}), {K,AllKnots[{3,10}]}]

Select[AllKnots[{3,10}], KnotGenus[#]<=1&]

Select[AllKnots[{3,10}], KnotGenus[#]<=2&]

FiberedKnots⋂AllKnots[{3,10}]

Ribbons⋂AllKnots[{3,10}]

Table[K->Factor[Θ[K]],{K,Ribbons⋂AllKnots[{3,10}]}]