Simplification Techniques for Maps in Simplicial Topology

TL;DR

This paper introduces algorithms to simplify complex maps in Simplicial Topology, enabling explicit combinatorial descriptions of Steenrod powers using face operators, thus reducing computational complexity.

Contribution

It provides novel algorithmic methods to derive economical formulas for cohomology maps, specifically simplifying Steenrod power computations in simplicial complexes.

Findings

Explicit combinatorial formulas for Steenrod k-th powers

Reduced computational complexity for cohomology operations

Algorithmic framework for simplifying simplicial maps

Abstract

This paper offers an algorithmic solution to the problem of obtaining "economical" formulae for some maps in Simplicial Topology, having, in principle, a high computational cost in their evaluation. In particular, maps of this kind are used for defining cohomology operations at the cochain level. As an example, we obtain explicit combinatorial descriptions of Steenrod k-th powers exclusively in terms of face operators.