{"paper":{"title":"Remarks about the Moebius-Kantor graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.GT","authors_text":"Oliver Knill","submitted_at":"2026-05-29T03:42:08Z","abstract_excerpt":"The Moebius-Kantor graph MK=G(8,3) is a Cayley graph of three non-abelian groups, the Pauli group P(1), the semi-dihedral group SD(16), as well as the dihedral group D(16) of order 16. In topological graph theory, it illustrates the Heawood number 7 of the torus and leads to the Tucker group Aut(MK), the unique group of genus 2. We compute the Lefschetz numbers to illustrate the Brouwer-Lefschetz fixed point theorem. MK is also the dual of the 2-skeleton complex of the 3-sphere G. The graph represents one of flat Clifford tori of a Hopf fibration in the 3-sphere G=K(2,2,2,2) reflecting that Co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30799","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.30799/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}