Surgery on tori in the 4-sphere

Abstract

We investigate the operation of torus surgery on tori embedded in $S^4$. 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 $S^4$.

18 pages, 4 figures. Second version includes minor changes and improvements, including some recommended by the referee. This paper has been accepted for publication in the Mathematical Proceedings of the Cambridge Philosophical Society

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