%0 Journal Article
%T The smooth structure set of $S^p \times S^q$
%A Diarmuid Crowley
%J Mathematics
%D 2009
%I arXiv
%X We calculate the smooth structure set of $S^p \times S^q$, $S(p, q)$, for $p, q \geq 2$ and $p+q \geq 5$. As a consequence we show that in general $S(4j-1, 4k)$ cannot admit a group structure such that the smooth surgery exact sequence is a long exact sequence of groups. We also show that the image of forgetful map $F: S(4j, 4k) --> S^{Top}(4j, 4k)$ is not in general a subgroup of the topological structure set.
%U http://arxiv.org/abs/0904.1370v2