On isotopy classification of embeddings of n-manifolds in [formula omitted

Abstract

In this paper the isotopy group of embeddings of an orientable closed manifold M in the real projective space of even dimension, a nonorientable manifold, in the metastable range, is computed in terms of the homotopy groups of M. The computation is based on the approach to embedding problems in normal bordism framework, which converts the calculations into those of singular homology groups of a certain elaborate space pair with twisted integers as coefficients. It forms part of a project which applies the normal bordism method to the existence and isotopy classification of differential embeddings of manifolds in manifolds in the metastable range.