Pseudo-isotopy classes of diffeomorphisms of the unknotted pairs $(S\sp {n+2},S\sp n)$ and $(S\sp {2p+2},S\sp p\times S\sp p)$

Abstract

We consider two pairs, the standard unknotted $n$-sphere in $S^{n+2}$, and the product of two $p$-spheres trivially embedded in $S^{2p+2}$, and study orientation preserving diffeomorphisms of these pairs. Pseudo-isotopy classes of such diffeomorphisms form subgroups of the mapping class groups of $S^n$ and $S^p\times S^p$, respectively, and we determine the algebraic structure of such subgroups when $n>4$ and $p>1$.