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arXiv · 2604.10192

Persistent Simple-homotopy invariants via discrete Morse theory

Divya Ahuja·Priyavrat Deshpande·Jaya NN Iyer·Siddharth Pritam
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Abstract

Persistent homology records the evolution of homological features along a filtration, but does not retain finer information related to simple-homotopy theory. In this paper, we develop two approaches to capturing such information for filtered simplicial complexes. We first introduce the Morse complexity profile, which records the minimal number of critical simplices at each filtration level. We study its invariance and stability properties and develop computable approximations using several discrete Morse matchings. We then introduce a persistent version of Whitehead torsion and show that it is invariant under both levelwise homotopy equivalence and interleaving equivalence of filtrations.

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Divya Ahuja, Priyavrat Deshpande, Jaya NN Iyer, Siddharth Pritam. 2026-09-22. Persistent Simple-homotopy invariants via discrete Morse theory. https://arxiv.org/abs/2604.10192

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