Persistent Simple-homotopy invariants via discrete Morse theory

Divya Ahuja; Jaya NN Iyer

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arXiv · 2604.10192

Persistent Simple-homotopy invariants via discrete Morse theory

Divya Ahuja·Jaya NN Iyer

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Abstract

We introduce a refinement of persistent homology that detects simple-homotopy-theoretic phenomena invisible to homology. Given a filtered simplicial complex, we define the Morse complexity profile as the minimal number of critical simplices at each filtration level. We prove that this profile is invariant under levelwise simple-homotopy equivalence and detects filtrations indistinguishable by persistent homology. We establish conditional stability under simple interleavings and provide an efficient algorithm for Vietoris-Rips filtrations. We also introduce a persistent version of Whitehead torsion and show that it is invariant under both levelwise simple-homotopy equivalence and interleaving equivalence of filtrations.

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Divya Ahuja, Jaya NN Iyer. 2026-04-11. Persistent Simple-homotopy invariants via discrete Morse theory. https://arxiv.org/abs/2604.10192

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