On transgression in associated bundles

TL;DR

This paper develops a general formula for transgressing characteristic forms in associated bundles, extending classical results and providing explicit formulas for important characteristic classes.

Contribution

It introduces a unified approach to transgression formulas in associated bundles, generalizing and deriving key classical results with explicit expressions.

Findings

Derived a general transgression formula for characteristic forms in associated bundles.

Provided explicit formulas for Johnson's transgression and Chern's Euler class transgression.

Extended classical transgression results to a broader bundle context.

Abstract

We formulate and prove a formula for transgressing characteristic forms in general associated bundles following a method of Chern. As applications, we derive D. Johnson's explicit formula for such general transgression and Chern's first transgression formula for the Euler class.