{"paper":{"title":"Composing generic linearly perturbed mappings and immersions/injections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Shunsuke Ichiki","submitted_at":"2016-12-04T11:13:14Z","abstract_excerpt":"Let $N$ (resp., $U$) be a manifold (resp., an open subset of $\\mathbb{R}^m$). Let $f:N\\to U$ and $F:U\\to \\mathbb{R}^\\ell$ be an immersion and a $C^{\\infty}$ mapping, respectively. Generally, the composition $F\\circ f$ does not necessarily yield a mapping transverse to a given subfiber-bundle of $J^1(N,\\mathbb{R}^\\ell)$. Nevertheless, in this paper, for any $\\mathcal{A}^1$-invariant fiber, we show that composing generic linearly perturbed mappings of $F$ and the given immersion $f$ yields a mapping transverse to the subfiber-bundle of $J^1(N,\\mathbb{R}^\\ell)$ with the given fiber. Moreover, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01100","kind":"arxiv","version":3},"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"}