On spherical fibrations and Poincare complexes

2024/06/23 by Wen Shen, Shen, Wen · 1 citation
Mathematics · #Graph theory and applications #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2406.16019

Abstract

In this paper, we prove that certain spherical fibrations over certain CW-complexes are stably fibre homotopy equivalent to \mmTOP-spherical fibrations (see Definition 1,1). Applying this result, we get a sufficient condition for whether a Poincar\mm\acutee 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\mm\acutee complexes.

Cited by

• Manifold structures on highly connected Poincaré complexes

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