{"paper":{"title":"A short proof of Gr\\\"unbaum's Conjecture about affine invariant points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Natalia Jonard-P\\'erez","submitted_at":"2016-02-21T18:19:22Z","abstract_excerpt":"Let us denote by $\\mathcal K_n$ the hyperspace of all convex bodies of $\\mathbb R^n$ equipped with the Hausdorff distance topology. An affine invariant point $p$ is a continuous and Aff(n)-equivariant map $p:\\mathcal K_n\\to \\mathbb R^n$, where Aff(n) denotes the group of all nonsingular affine maps of $\\mathbb R^n$. For every $K\\in\\mathcal K_n$, let $\\mathfrak{P}_n(K)=\\{p(K)\\in\\mathbb R^n\\mid p\\text{ is an affine invariant point}\\}$ and $\\mathfrak{F}_n(K)=\\{x\\in\\mathbb R^n\\mid gx=x\\text{ for every }g\\in Aff(n)\\text{ such that }gK=K\\}$. In 1963, B. Gr\\\"unbaum conjectured that $\\mathfrak{P}_n(K)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06560","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"}