Classifies smooth closed oriented manifolds homotopy equivalent to three families of sphere products up to almost diffeomorphism by realizing the image of the normal-invariant map with explicit constructions from bundles and plumbings.
The smooth structure set of $S^p \times S^q$
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abstract
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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Smooth manifolds homotopy equivalent to products of spheres
Classifies smooth closed oriented manifolds homotopy equivalent to three families of sphere products up to almost diffeomorphism by realizing the image of the normal-invariant map with explicit constructions from bundles and plumbings.