Manifolds that admit a double disk-bundle decomposition

TL;DR

This paper proves that certain low-dimensional, simply connected manifolds with a double disk-bundle decomposition are rationally elliptic, and classifies them explicitly in dimensions five and six under specific conditions.

Contribution

It establishes rational ellipticity for these manifolds and provides a classification in dimensions five and six under particular Betti number constraints.

Findings

Manifolds with double disk-bundle decompositions are rationally elliptic in dimensions ≤7.

Complete classification of such manifolds in dimension five.

Classification in dimension six under specific Betti number conditions.

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.