Torus Topology

(p,q)-torus knot: gcd=1 knot
A (p,q)-torus curve winds p times around the torus in the toroidal direction and q times in the poloidal direction. When gcd(p,q)=1, it is a knot (connected). When gcd(p,q)=d>1, it splits into d linked components. The fundamental group π₁(T²) = ℤ × ℤ, generated by these two loops.