{"paper":{"title":"On Shift Dynamics For Cyclically Presented Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"William A. Bogley","submitted_at":"2013-12-19T00:56:14Z","abstract_excerpt":"For group presentations with cyclic symmetry, there is a connection between asphericity and the dynamics of the shift automorphism. For the class of groups $G_n(k,l)$ described by the cyclic presentations $\\mathcal{P}_n(k,l) = (x_i:x_ix_{i+k}x_{i+l}\\ (i \\mod n))$ and studied extensively by G. Williams and M. Edjvet \\cite{EdjvetWilliams}, the shift acts freely on the nonidentity elements of $G_n(k,l)$ if and only if the presentation $\\mathcal{P}_n(k,l)$ is combinatorially aspherical in the sense of \\cite{CCH}. The shift has a nonidentity fixed point precisely when $G_n(k,l)$ is finite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5382","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"}