{"paper":{"title":"Equilateral $p$-gons in $\\mathbb R^d$ and deformed spheres and mod $p$ Fadell-Husseini index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Andr\\'es Angel, Jerson Borja","submitted_at":"2017-06-06T06:26:57Z","abstract_excerpt":"We introduce the concept of $r$-equilateral $m$-gons. We prove the existence of $r$-equilateral $p$-gons in $\\mathbb R^d$ if $r<d$ and the existence of equilateral $p$-gons in the image of continuous injective maps $f:S^d\\to \\mathbb R^{d+1}$. Our ideas are based mainly in the paper of Y. Soibelman \\cite{soibelman}, in which the topological Borsuk number of $\\mathbb{R}^2$ is calculated by means of topological methods and the paper of P. Blagojevi\\'c and G. Ziegler \\cite{blagojevictetrahedra} where Fadell-Husseini index is used for solving a problem related to the topological Borsuk problem for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01618","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"}