Persistent Simple-homotopy invariants via discrete Morse theory
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908954998603776 |
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| author | Ahuja, Divya Iyer, Jaya NN |
| author_facet | Ahuja, Divya Iyer, Jaya NN |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10192 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Persistent Simple-homotopy invariants via discrete Morse theory Ahuja, Divya Iyer, Jaya NN Algebraic Topology 55N31, 57Q10, 57Q70, 55P10, 68U05 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. |
| title | Persistent Simple-homotopy invariants via discrete Morse theory |
| topic | Algebraic Topology 55N31, 57Q10, 57Q70, 55P10, 68U05 |
| url | https://arxiv.org/abs/2604.10192 |