On the Rothenberg-Steenrod spectral sequence for the mod 3 cohomology of the classifying space of the exceptional Lie group E_8

TL;DR

This paper demonstrates that the Rothenberg-Steenrod spectral sequence for the mod 3 cohomology of the classifying space of the exceptional Lie group E_8 does not collapse at the E_2 stage, revealing complex algebraic structure.

Contribution

It provides the first proof that the spectral sequence does not collapse at E_2 for this specific case, advancing understanding of E_8's cohomology.

Findings

Spectral sequence does not collapse at E_2 for E_8

Reveals complex structure in mod 3 cohomology of E_8

Enhances understanding of algebraic topology of exceptional Lie groups

Abstract

We show that the Rothenberg--Steenrod spectral sequence converging to the mod 3 cohomology of the classifying space of the exceptional Lie group E_8 does not collapse at the E_2-level.