{"paper":{"title":"Quaternionic Hyperbolic Fenchel-Nielsen Coordinates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Krishnendu Gongopadhyay, Sagar B. Kalane","submitted_at":"2017-08-21T01:16:25Z","abstract_excerpt":"Let $Sp(2,1)$ be the isometry group of the quaternionic hyperbolic plane ${{\\bf H}_{\\mathbb H}}^2$. An element $g$ in $Sp(2,1)$ is `hyperbolic' if it fixes exactly two points on the boundary of ${{\\bf H}_{\\mathbb H}}^2$. We classify pairs of hyperbolic elements in $Sp(2,1)$ up to conjugation.\n  A hyperbolic element of $Sp(2,1)$ is called `loxodromic' if it has no real eigenvalue. We show that the set of $Sp(2,1)$ conjugation orbits of irreducible loxodromic pairs is a $(\\mathbb C {\\mathbb P}^1)^4$-bundle over a topological space that is locally a semi-analytic subspace of ${\\mathbb R}^{13}$. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06044","kind":"arxiv","version":3},"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"}