An Elementary Classification of Symmetric 2-Cocycles

TL;DR

This paper classifies additive symmetric 2-cocycles over Z/p, expanding on prior work to provide a comprehensive understanding with implications for algebraic topology and formal group laws.

Contribution

It offers a new classification of symmetric 2-cocycles over Z/p and presents partial results and conjectures for higher m-cocycles, extending previous foundational work.

Findings

Complete classification of 2-cocycles over Z/p.

Partial results and conjectures for m-cocycles, m > 2.

Applications to algebraic topology and formal group laws.

Abstract

We present a classification of the so-called "additive symmetric 2-cocycles" of arbitrary degree and dimension over Z/p, along with a partial result and some conjectures for m-cocycles over Z/p, m > 2. This expands greatly on a result originally due to Lazard and more recently investigated by Ando, Hopkins, and Strickland, which together with their work culminates in a complete classification of 2-cocycles over an arbitrary commutative ring. The ring classifying these polynomials finds application in algebraic topology, including generalizations of formal group laws and of cubical structures.