Milnor operations and classifying spaces

TL;DR

This paper presents a counterexample in algebraic topology showing a specific element in a classifying space where all higher Milnor operations vanish, challenging a previous conjecture.

Contribution

It provides the first known counterexample to a conjecture by Kono and Yagita regarding Milnor operations on classifying spaces.

Findings

Identifies a nonzero odd degree element with vanishing higher Milnor operations.

Challenges the conjecture of Kono and Yagita.

Expands understanding of the structure of classifying spaces.

Abstract

We give an example of a nonzero odd degree element of the classifying space of a connected Lie group such that all higher Milnor operations vanish on it. It is a counterexample for a conjecture of Kono and Yagita.