On the Rothenberg-Steenrod spectral sequence for the mod 2 cohomology of classifying spaces of spinor groups

TL;DR

This paper computes the cotorsion product for the mod 2 cohomology of spinor groups and demonstrates that the Rothenberg-Steenrod spectral sequence does not collapse for n > 16, revealing new structural insights.

Contribution

It provides the first explicit computation of the cotorsion product for spin(n) and shows the spectral sequence's non-collapsing behavior for large n.

Findings

Cotorsion product computed for spin(n)

Spectral sequence does not collapse for n > 16

New structural understanding of mod 2 cohomology of spinor groups

Abstract

We compute the cotorsion product of the mod 2 cohomology of spinor group spin(n), which is the E_2-term of the Rothenberg-Steenrod spectral sequence for the mod 2 cohomology of the classifying space of the spinor group spin(n). As a consequence of this computation, we show the non-collapsing of the Rothenberg-Steenrod spectral sequence for n > 16.