{"paper":{"title":"On the automorphism group of the Morse complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Maxwell Lin, Nicholas A. Scoville","submitted_at":"2019-04-24T16:29:06Z","abstract_excerpt":"Let $K$ be a finite, connected, abstract simplicial complex. The Morse complex of $K$, first introduced by Chari and Joswig, is the simplicial complex constructed from all gradient vector fields on $K$. We show that if $K$ is neither the boundary of the $n$-simplex nor a cycle, then $\\mathrm{Aut}(\\mathcal{M}(K))\\cong \\mathrm{Aut}(K)$. In the case where $K= C_n$, a cycle of length $n$, we show that $\\mathrm{Aut}(\\mathcal{M}(C_n))\\cong \\mathrm{Aut}(C_{2n})$. In the case where $K=\\partial\\Delta^n$, we prove that $\\mathrm{Aut}(\\mathcal{M}(\\partial\\Delta^n))\\cong \\mathrm{Aut}(\\partial\\Delta^n)\\time"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10907","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}