Topological properties of high-dimensional handles

We investigate the group of orientation-preserving auto-homeomorphisms resp. homotopy self-equivalences of the connected sum X of p copies of S^1 x S^n, for p greater than or equal 1, modulo those pseudo-isotopic resp. homotopic to the identity. This result is related to a paper of Hosokawa and Kawauchi on unknotted surfaces in Euclidean 4-space, published in Osaka J. Math. 16 (1979), extending it (in greater generality) for embeddings of X into Euclidean (n+3)-space. Finally, we classify the homotopy type of the complement of an embedded copy of X into the Euclidean (n+3)-space, giving examples of manifolds homotopy equivalent to a bouquet of spheres which cannot be fibered over a circle.