In 1986, S. Boyer generalized Freedman's result to simply-connected topological 4 manifolds with boundaries. He proved in many cases, the intersection form and the boundary determine the homeomorphism types of the 4 manifolds. In this thesis, we will study simply-connected smooth 4 manifolds with boundaries by using handlebody techniques. We will show that: there do exist simply-connected smooth 4 manifolds with the same intersection form and the same boundary but not homeomorphic to each other, and the cause of this phenomenon is ``Plug''.
Read
