Persistence Steenrod modules
Abstract
Domain fit: Niche / domain-specific · No strong AI-core implementation/artifact signals were detected from current providers.
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 $$Sq^k$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:msup><mml:mi>q</mml:mi><mml:mi>k</mml:mi></mml:msup></mml:mrow></mml:math> -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.
Results and benchmarks
Abstract It has long been envisioned that the strength of the barcode invariant of filtered cellular complexes could be increased using cohomology operations.
Benchmark evidence is limited
Evidence graph: 2 refs, 1 links.
Utility signals: depth 65/100, grounding 58/100, status medium.
Implementation
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Time to first repro: a few days
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Validation caveat
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Research context
14
Citations
35
References
Tasks
Cohomology, Computation, Barcode, Computer science, persistent cohomology, Steenrod squares, mod 2 cohomology, cohomology operations
Methods
Algorithm
Domains
Invariant (physics), Mathematics, Computational Theory and Mathematics
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