On the Classification of $S^3$-Bundles over $\mathbb{C}P^2$
Algebraic Topology
2025-12-02 v2 Geometric Topology
Abstract
This paper presents a classification of the total spaces of -bundles over up to orientation-preserving homotopy equivalence. Our approach proceeds in two steps: we first derive the PL-homeomorphism classification for these manifolds by computing their Kreck-Stolz invariants. Then, building upon this PL classification result and through an application of surgery theory, we establish the homotopy equivalence classification.
Keywords
Cite
@article{arxiv.2511.22999,
title = {On the Classification of $S^3$-Bundles over $\mathbb{C}P^2$},
author = {Wancheng Liu},
journal= {arXiv preprint arXiv:2511.22999},
year = {2025}
}