Smooth manifolds homotopy equivalent to products of spheres

Sagnik Biswas

paper

Smooth manifolds homotopy equivalent to products of spheres

arXiv:2606.10239

Abstract

We classify, up to almost diffeomorphism, the smooth closed oriented manifolds homotopy equivalent to each of the sphere products $S^{4 k - 1} \times S^{4 k}$ , $S^{4 k} \times S^{4 k}$ , and $S^{4 k} \times S^{4 k + 1}$ . In each case we realize the image of the normal-invariant map in the smooth surgery exact sequence by explicit families of manifolds: sphere bundles over $S^{4 k}$ ; pinch maps and Milnor plumbings of disk bundles; and Novikov sphere bundles together with connected sums of homotopy spheres.