{"paper":{"title":"Open book structures on semi-algebraic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.AG","authors_text":"Antonio Andrade (ICMC), Nicolas Dutertre (I2M), Raimundo N. Ara\\'ujo Dos Santos (ICMC), Ying Chen (ICMC)","submitted_at":"2014-09-15T16:43:52Z","abstract_excerpt":"Given a $C^2$ semi-algebraic mapping $F: \\mathbb{R}^N \\rightarrow \\mathbb{R}^p,$ we consider its restriction to $W\\hookrightarrow \\mathbb{R^{N}}$ an embedded closed semi-algebraic manifold of dimension $n-1\\geq p\\geq 2$ and introduce sufficient conditions for the existence of a fibration structure (generalized open book structure) induced by the projection $\\frac{F}{\\Vert F \\Vert}:W\\setminus F^{-1}(0)\\to S^{p-1}$. Moreover, we show that the well known local and global Milnor fibrations, in the real and complex settings, follow as a byproduct by considering $W$ as spheres of small and big radii"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4316","kind":"arxiv","version":2},"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"}