On automorphisms of high-dimensional solid tori

We study the infinite generation in the homotopy groups of the group of diffeomorphisms of S 1 × D 2n-1 , for 2n ≥ 6, in a range of degrees up to n -2.Our analysis relies on understanding the homotopy fibre of a linearisation map from the plusconstruction of the classifying space of a certain space of self-embeddings of stabilisations of this manifold to a form of Hermitian K-theory of the integral group ring of π1(S 1 ).We also show that these homotopy groups vanish rationally.