An Elementary Introduction to the Hopf Fibration
... Consider the point (1, 0, 0) in S 2 . One can easily check that the set of points C = {(cos t, sin t, 0, 0) | t ∈ R} in S 3 all map to (1, 0, 0) via the Hopf map h. In fact, this set C is the entire set of points that map to (1, 0, 0) via h. In other words, C is the preimage set h −1 ((1, 0, 0)). Yo ...
... Consider the point (1, 0, 0) in S 2 . One can easily check that the set of points C = {(cos t, sin t, 0, 0) | t ∈ R} in S 3 all map to (1, 0, 0) via the Hopf map h. In fact, this set C is the entire set of points that map to (1, 0, 0) via h. In other words, C is the preimage set h −1 ((1, 0, 0)). Yo ...
