{"paper":{"title":"Vanishing polyhedron and collapsing map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Aur\\'elio Menegon Neto, L\\^e D\\~ung Tr\\'ang","submitted_at":"2015-11-21T01:42:57Z","abstract_excerpt":"In this paper we give a detailed proof that the Milnor fiber $X_t$ of an analytic complex isolated singularity function defined on a reduced $n$-equidimensional analytic complex space $X$ is a regular neighborhood of a polyhedron $P_t \\subset X_t$ of real dimension $n-1$. Moreover, we describe the degeneration of $X_t$ onto the special fiber $X_0$, by giving a continuous collapsing map $\\Psi_t: X_t \\to X_0$ which sends $P_t$ to $\\{0\\}$ and which restricts to a homeomorphism $X_t \\backslash P_t \\to X_0 \\backslash \\{0\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06812","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"}