Computing Adem Cohomology Operations

TL;DR

This paper develops explicit formulas and algorithms to compute Adem cohomology operations directly at the cochain level for finite simplicial sets, facilitating practical calculations in algebraic topology.

Contribution

It introduces explicit simplicial formulas for Adem cohomology operations and an algorithm to compute them for any finite simplicial set, advancing computational methods in topology.

Findings

Explicit formulas for Adem cohomology operations at the cochain level

An algorithm for computing these operations on finite simplicial sets

Enhanced computational tools for algebraic topology

Abstract

We deal with the problem of obtaining explicit simplicial formulae defining the classical Adem cohomology operations at the cochain level. Having these formulae at hand, we design an algorithm for computing these operations for any finite simplicial set.