{"paper":{"title":"On Globally Diffeomorphic Polynomial Maps via Newton Polytopes and Circuit Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Oliver Stein, Tomas Bajbar","submitted_at":"2016-02-05T10:57:07Z","abstract_excerpt":"In this article we analyze the global diffeomorphism property of polynomial maps $F:\\mathbb{R}^n\\rightarrow\\mathbb{R}^n$ by studying the properties of the Newton polytopes at infinity corresponding to the sum of squares polynomials $\\|F\\|_2^2$. This allows us to identify a class of polynomial maps $F$ for which their global diffeomorphism property on $\\mathbb{R}^n$ is equivalent to their Jacobian determinant $\\text{det }JF$ vanishing nowhere on $\\mathbb{R}^n$. In other words, we identify a class of polynomial maps for which the Real Jacobian Conjecture, which was proven to be false in general,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01977","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"}