{"paper":{"title":"The Disk-Based Origami Theorem and a Glimpse of Holography for Traversing Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Gabriel Katz","submitted_at":"2018-10-06T18:06:02Z","abstract_excerpt":"This paper describes a mechanism by which a traversally generic flow $v$ on a smooth connected manifold $X$ with boundary produces a compact $CW$-complex $\\mathcal T(v)$, which is homotopy equivalent to $X$ and such that $X$ embeds in $\\mathcal T(v)\\times \\mathbf R$. The $CW$-complex $\\mathcal T(v)$ captures some residual information about the smooth structure on $X$ (such as the stable tangent bundle of $X$). Moreover, $\\mathcal T(v)$ is obtained from a simplicial \\emph{origami map} $O: D^n \\to \\mathcal T(v)$, whose source space is a disk $D^n \\subset \\partial X$ of dimension $n = \\dim(X) -1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04023","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"}