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Smooth manifolds homotopy equivalent to products of spheres
Abstract
We classify, up to almost diffeomorphism, the smooth closed oriented manifolds homotopy equivalent to each of the sphere products S4k−1× S4k, S4k× S4k, and S4k× S4k+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 S4k; pinch maps and Milnor plumbings of disk bundles; and Novikov sphere bundles together with connected sums of homotopy spheres.
Related
- On smooth and bundle structures on topological manifolds homotopy equivalent to S4k−1-bundles over S4k
- Simple homotopy types of smooth four-manifolds with finite fundamental group
- New families of moment-angle manifolds diffeomorphic to connected sums of products of spheres
- Homotopy groups of spheres and dimension quotients
- Some homotopy coherent finite group actions on spheres
BibTeX
@misc{biswas2026smooth,
title = {{Smooth manifolds homotopy equivalent to products of spheres}},
author = {Sagnik Biswas},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.10239},
eprint = {2606.10239},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.10239},
}
RIS
TY - UNPB
TI - Smooth manifolds homotopy equivalent to products of spheres
AU - Sagnik Biswas
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2606.10239
UR - https://arxiv.org/abs/2606.10239
AB - We classify, up to almost diffeomorphism, the smooth closed oriented manifolds homotopy equivalent to each of the sphere products S^4k−1× S^4k, S^4k× S^4k, and S^4k× S^4k+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^4k; pinch maps and Milnor plumbings of disk bundles; and Novikov sphere bundles together with connected sums of homotopy spheres.
ER -