English

On spherical fibrations and Poincare complexes

Geometric Topology 2025-04-01 v2 Algebraic Topology

Abstract

In this paper, we prove that certain spherical fibrations over certain CW-complexes are stably fibre homotopy equivalent to \mmTOP\mm{TOP}-spherical fibrations (see Definition 1,1). Applying this result, we get a sufficient condition for whether a Poincar\mmeˊ\mm{\acute{e}} complex is of the homotopy type of a topological manifold. Moreover, we present the classification for some highly connected manifolds by the homotopy types of highly connected Poincar\mmeˊ\mm{\acute{e}} complexes.

Keywords

Cite

@article{arxiv.2406.16019,
  title  = {On spherical fibrations and Poincare complexes},
  author = {Wen Shen},
  journal= {arXiv preprint arXiv:2406.16019},
  year   = {2025}
}
R2 v1 2026-06-28T17:16:09.609Z