The smooth structure set of $S^p \times S^q$

Mathematics – Geometric Topology

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21 pages. Referee's suggestions included, proof of Lemma 4.1 clarified, typos corrected. To appear in Geometriae Dedicata

Scientific paper

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.

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