
TL;DR
This paper studies how torus surgeries in the 4-sphere can produce various 4-manifolds, explores their uniqueness, and constructs new embeddings of 3-manifolds, including homology spheres, into 4-manifolds.
Contribution
It introduces methods for torus surgery in $S^4$, analyzes the resulting 4-manifolds, and provides new embeddings of 3-manifolds, expanding understanding of 4-dimensional topology.
Findings
Characterization of 4-manifolds obtainable via torus surgery
Results on the uniqueness of torus surgery descriptions
New embeddings of homology spheres into $S^4$
Abstract
We investigate the operation of torus surgery on tori embedded in . 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 .
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