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 -spherical fibrations (see Definition 1,1). Applying this result, we get a sufficient condition for whether a Poincar 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 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}
}