Spectral sequence operations converge to Araki-Kudo operations

TL;DR

This paper demonstrates that spectral sequence operations in mod 2 homology converge to the classical Araki-Kudo operations in the homology of the total space of a cosimplicial E-infinity space, confirming their compatibility.

Contribution

It establishes the convergence of spectral sequence operations to Araki-Kudo operations and shows their agreement with the multiplication in the homology of Tot X.

Findings

Spectral sequence operations match Araki-Kudo operations in the target.

Operations agree with the multiplication in H_*(Tot X).

Convergence of spectral sequence operations is proven.

Abstract

Previously we constructed operations in the mod 2 homology spectral sequence associated to a cosimplicial E-infinity space X. The correct target for this spectral sequence is the homology of Tot X. Noting that in this setting Tot X is an E-infinity space, we show that our operations agree with the usual Araki-Kudo operations in the target. We also prove that the multiplication in the spectral sequence agrees with the multiplication in H_*(Tot X).