Surgery on tori in the 4–sphere

Abstract

AbstractWe investigate the operation of torus surgery on tori embedded in S4. Key questions include which 4–manifolds can be obtained in this way, and the uniqueness of such descriptions. As an application we construct embeddings of 3–manifolds into 4–manifolds by viewing Dehn surgery as a cross section of a surgery on a surface. In particular, we give new embeddings of homology spheres into S4.