{"paper":{"title":"On discreteness of subgroups of quaternionic hyperbolic isometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.GT","authors_text":"Devendra Tiwari, Krishnendu Gongopadhyay, Mukund Madhav Mishra","submitted_at":"2018-10-01T12:31:52Z","abstract_excerpt":"Let ${{\\bf H}_{\\mathbb H}}^n$ denote the $n$-dimensional quaternionic hyperbolic space. The linear group ${\\rm{Sp}}(n,1)$ acts by the isometries of ${{\\bf H}_{\\mathbb H}}^n$. A subgroup $G$ of ${\\rm {Sp}}(n,1)$ is called \\emph{Zariski dense} if it does not fix a point on ${{\\bf H}_{\\mathbb H}}^n \\cup \\partial {{\\bf H}_{\\mathbb H}}^n$ and neither it preserves a totally geodesic subspace of ${{{\\bf H}}_{\\mathbb H}}^n$. We prove that a Zariski dense subgroup $G$ of ${\\rm{ Sp}}(n,1)$ is discrete if for every loxodromic element $g \\in G$ the two generator subgroup $\\langle f, g f g^{-1} \\rangle$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00657","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"}