Persistence Steenrod modules

Understand

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.