On the Homomorphisms of the Lie Groups SU(2)‎ and S3

Abstract EN

We first construct all the homomorphisms from the Heisenberg group to the 3-sphere.

Also, defining a topology on these homomorphisms, we regard the set of these homomorphisms as a topological space.

Next, using the kernels of homomorphisms, we define an equivalence relation on this topological space.

We finally show that the quotient space is a topological group which is isomorphic to ?1.