{"paper":{"title":"Dynamical Deformation of Toroidal Matrix Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MG"],"primary_cat":"math.OA","authors_text":"Fredy Vides","submitted_at":"2015-06-24T17:11:24Z","abstract_excerpt":"In this document we study the local connectivity of the sets whose elements are $m$-tuples of pairwise commuting normal matrix contractions. Given $\\varepsilon>0$, we prove that there is $\\delta>0$ such that for any two $m$-tuples of pairwise commuting normal matrix contractions $\\mathbf{X}:=(X_1,\\ldots,X_m)$ and $\\tilde{\\mathbf{X}}:=(\\tilde{X}_1,\\ldots,\\tilde{X}_m)$ that are $\\delta$-close with respect to some suitable distance $\\eth$ in $(\\mathbb{C}^{n\\times n})^m$, we can find a $m$-tuple of matrix paths (homotopies) connecting $\\mathbf{X}$ to $\\mathbf{\\tilde{X}}$ relative to the intersecti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07470","kind":"arxiv","version":4},"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"}