  Cappell-Shaneson homotopy 4-spheres (CS spheres) are potential
counterexamples of the smooth 4-dimensional Poincar\'e conjecture. Akbulut
proved that infinite CS spheres are diffeomorphic to the standard 4-sphere by
Kirby calculus. Kim and Yamada found another family of CS spheres which is
composed of standard CS spheres. In this paper, we prove more CS spheres are
standard. We give 145 new infinite families of CS spheres which are
diffeomorphic to the standard 4-sphere.
