Manifold with infinitely many fibrations over the sphere

TL;DR

The paper demonstrates that the manifold S^2×S^3 admits infinitely many fiber bundle structures over S^2, including fibrations with various lens spaces as fibers, revealing rich topological diversity.

Contribution

It establishes the existence of infinitely many fiber bundle structures over S^2 on the manifold S^2×S^3, including fibrations with lens spaces as fibers.

Findings

S^2×S^3 has infinitely many fiber bundle structures over S^2.

For each lens space L(p,1), there exists a fibration over S^2 with fiber L(p,1).

The manifold admits a diverse set of topological fibrations.

Abstract

We show that the manifold $X=S^2\times S^3$ has infinitely many structures of a fiber bundle over the base $B=S^2.$ In fact for every lens space $L(p,1)$ there is a fibration $L(p,1)\to X\to B.$