Manifolds that admit a double disk-bundle decomposition
Differential Geometry
2022-03-14 v2 Geometric Topology
Abstract
Under mild topological restrictions, this article establishes that a smooth, closed, simply connected manifold of dimension at most seven which can be decomposed as the union of two disk bundles must be rationally elliptic. In dimension five, such manifolds are classified up to diffeomorphism, while the same is true in dimension six when either the second Betti number vanishes or the third Betti number is non-trivial.
Cite
@article{arxiv.2008.10278,
title = {Manifolds that admit a double disk-bundle decomposition},
author = {Jason DeVito and Fernando Galaz-Garcia and Martin Kerin},
journal= {arXiv preprint arXiv:2008.10278},
year = {2022}
}
Comments
38 pages, final version. To appear in the Indiana University Journal of Mathematics