Orientable 4-dimensional Poincar\'e Complexes have Reducible Spivak Fibrations

TL;DR

This paper proves that orientable 4-dimensional Poincaré complexes have Spivak normal fibrations that can be reduced to vector bundles, advancing understanding of their topological structure.

Contribution

It establishes that the Spivak normal fibration of such complexes admits a vector bundle reduction, a new result in the topology of Poincaré complexes.

Findings

Spivak normal fibrations are reducible to vector bundles in orientable 4-dimensional Poincaré complexes.

The result enhances the classification understanding of these complexes.

Provides tools for further topological and geometric analysis.

Abstract

We show that the Spivak normal fibration of an orientable 4-dimensional Poincar\'e complex has a vector bundle reduction.