Extendibility and stable extendibility of normal bundles associated to immersions of real projective spaces (Q696154)

Let \(X\) be a space and \(A\) be a subspace of \(X\). A \(p\)-dimensional \(F\)-vector bundle \(\xi\) over \(A\) is called extendible (respectively stably extendible) to \(X\), if there is a \(p\)-dimensional \(F\)-vector bundle over \(X\) whose restriction to \(A\) is equivalent (respectively stably equivalent) to \(\xi\) as \(F\)-vector bundles (where \(F\) denotes the real field \(\mathbb{R}\), the complex field \(\mathbb{C}\) or the quaternionic field \(\mathbb{H}\)). Let \(\nu\) be the normal bundle associated to an immersion of the real projective space \(\mathbb{R} P^n\) in the Euclidean space \(\mathbb{R}^{n+k}\) (where \(k\) is any positive integer). In the paper under review, the authors determine the necessary and sufficient conditions for the stable extendibility of \(\nu\) and of its complexification \(c\nu\).