Even more Cappell-Shaneson spheres are standard

This thesis examines an important problem in the field of differential topology: the 4-dimensional smooth Poincaré conjecture. More specifically we analyze a class of objects known as Cappell-Shaneson spheres and the question of whether or not they are counterexamples to the conjecture. We prove some results which expand the class of Cappell-Shaneson spheres that are known to be standard. In addition, we find some interesting patterns in Cappell-Shaneson matrices which may provide useful directions for further research into the question of whether or not the associated manifolds are standard.Mathematic