On smooth and bundle structures on topological manifolds homotopy equivalent to $S^{4k-1}$-bundles over $S^{4k}$
Year: 2026
Type: preprint
Abstract: We first verify the expected calculations of the topological structure set, in the sense of surgery theory, for the total spaces of $S^{4k-1}$-bundles over $S^{4k}$ for $k\ge3$, in which manifolds homotopy equivalent to the total spaces are organized. Next, we investigate the question of which of the elements in these structure sets can be realized as such bundles. Moreover, we study the forgetful map from the smooth version to the topological version of the structure set; we determine its image. All elements in the image turn out to have the underlying manifold such a bundle.
Source: arXiv (Cornell University)
Authors: Raj, Ajay, Macko, Tibor
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213395560