Cohomology mod 3 of the classifying space of the exceptional Lie group $E_6$, I : structure of Cotor

TL;DR

This paper investigates the algebraic structure of the E_2-term in a spectral sequence used to compute the mod 3 cohomology of the classifying space of the exceptional Lie group E_6, revealing detailed cohomological properties.

Contribution

It provides a detailed analysis of the Cotor algebra structure in the spectral sequence for E_6's classifying space, advancing understanding of its cohomology.

Findings

Determined the structure of the E_2-term in the spectral sequence.

Identified algebraic relations within the Cotor algebra.

Enhanced the understanding of E_6's cohomological invariants.

Abstract

We study the structure of the $E_2$-term of the Rothenberg-Steenrod spectral sequence converging to the mod 3 cohomology of the classifying space of the compact, connected, simply connected, exceptional Lie group of rank 6.