Homogeneous spaces without taut embeddings (Q1113472)

The main theorem of the paper says that if \(M\subseteq E^ N\) is a taut submanifold with respect to a field F then the first non-trivial homology \(H_ i(M)\), \(i>0\), has no torsion other than of order two. In particular there are no taut 3-manifolds with respect to \({\mathbb{Z}}_ p\), \(p\geq 3\), which are not taut with respect to \({\mathbb{Z}}_ 2\). Many examples are given of homogeneous spaces with such torsion which consequently do not admit taut embeddings. Particular cases are the lens spaces L(p,1) except \(L(2,1)\cong {\mathbb{R}}P^ 3.\) The corresponding question for tight submanifolds seems still to be open.