Taut 3-manifolds (Q1262554)

This paper completes the classification up to diffeomorphism of those compact three-dimensional manifolds that admit taut embeddings into some Euclidean space. There are seven such manifolds: \(S^ 1\times S^ 2\), \(S^ 1\times {\mathbb{R}}P^ 2\), \(S^ 1\times_ hS^ 2\), where h denotes an orientation reversing diffeomorphism, \(S^ 3\), \({\mathbb{R}}P^ 3\), the quaternion space \(S^ 3/\{\pm 1,\quad \pm i,\quad \pm j,\quad \pm k\},\) and the torus \(T^ 3\). The complete geometric classification remains an open problem.