# Persistence Steenrod modules

## TL;DR

This paper introduces a new family of computable invariants called $Sq^k$-barcodes for mod 2 persistent cohomology, enhancing the discriminative power of barcode invariants in topological data analysis.

## Contribution

It presents the first complete algorithmic pipeline for computing $Sq^k$-barcodes and demonstrates their applicability on molecular conformation data.

## Key findings

- $Sq^k$-barcodes improve topological data analysis.
- Algorithm successfully applied to cyclo-octane molecule.
- Enhances the discriminative power of persistent invariants.

## Abstract

It has long been envisioned that the strength of the barcode invariant of filtered cellular complexes could be increased using cohomology operations. Leveraging recent advances in the computation of Steenrod squares, we introduce a new family of computable invariants on mod 2 persistent cohomology termed $Sq^k$-barcodes. We present a complete algorithmic pipeline for their computation and illustrate their real-world applicability using the space of conformations of the cyclo-octane molecule.