Algebraic independence of topological Pontryagin classes

TL;DR

This paper proves that topological Pontryagin classes are algebraically independent in the rationalized cohomology of BTop(d) for all dimensions d ≥ 4, advancing understanding of their algebraic structure.

Contribution

It establishes the algebraic independence of topological Pontryagin classes in the rationalized cohomology for all relevant dimensions, a previously unresolved question.

Findings

Topological Pontryagin classes are algebraically independent in BTop(d)

Independence holds for all dimensions d ≥ 4

Results apply to rationalized cohomology

Abstract

We show that the topological Pontryagin classes are algebraically independent in the rationalised cohomology of BTop(d) for all $d \geq 4$.