Strong Approximation for the Relative Character Variety of the Four-Times Punctured Sphere

Nathaniel Kingsbury-Neuschotz

We study the orbits of solutions to the Markoff-type equation $$X^2+Y^2+Z^2=XYZ+AX+BY+CZ+D$$ in ${\mathbb{F}}_p,$ for fixed integers $A,B,C,D,$ under the symmetry gr…