Regard the 3-sphere S^3 as a locus of points in C^2, (x_1+ix_2, x_3+ix_4) satisfying x^2_1+x^2_2 x^2_3+x^2_4=1. The multiplicative group U(1)=[z\in{C}| |z|=1] acts on C^2 by scalar multiplication.
Check that this action restricts to an action on S^3 then show that the quotient of S^3 by U(1) is homeomorphic to S^2.
Show that the preimage of each point in the quotient is homeomorphic to S^1 and that the preimages corresponding to any two distinct points in S^2 are linked in S^3