On the classification of oriented 3-plane bundles over a 6-complex

TL;DR

This paper completes the classification of certain 3-plane bundles over 6-dimensional complexes by correcting previous errors in characteristic class descriptions, advancing the understanding of bundle topology.

Contribution

It provides a corrected and complete description of low-degree characteristic classes for oriented 3-plane bundles over 6-complexes, addressing errors in prior work.

Findings

Corrected classification of characteristic classes

Clarified the structure of 3-plane bundles over 6-complexes

Resolved inaccuracies in previous literature

Abstract

In this short note, we complete the description of low-degree characteristic classes of oriented 3-plane bundles over a 6-complex. Our goal is to point out and correct an error in L. M. Woodward's 1982 paper "The classification of principal PU_n-bundles over a 4-complex."