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arXiv · 2509.16102

Lifting Cocycles: From Heuristic to Theory

Sigurd Gaukstad·Mathias Karsrud Nordal·Marius Thaule
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Abstract

The circular coordinates algorithm, a key tool in topological data analysis, relies on a theoretically unvalidated lifting step to convert cocycles from a prime field to integer coefficients. We provide a rigorous analysis of this procedure, establishing a criterion for its success. We also introduce a novel algebraic method to reduce any lifted cocycle to a cocycle with winding number 1, ensuring feature correctness. These principles are extended to homology cycles, solidifying the theoretical foundation of this widely used feature extraction technique.

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Sigurd Gaukstad, Mathias Karsrud Nordal, Marius Thaule. 2025-09-19. Lifting Cocycles: From Heuristic to Theory. https://arxiv.org/abs/2509.16102

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