{"paper":{"title":"Groups acting on products of trees, tiling systems and analytic K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Guyan Robertson, Jason S. Kimberley","submitted_at":"2013-02-23T10:11:43Z","abstract_excerpt":"Let $T_1$ and $T_2$ be homogeneous trees of even degree $\\ge 4$. A BM group $\\Gamma$ is a torsion free discrete subgroup of $\\aut (T_1) \\times \\aut (T_2)$ which acts freely and transitively on the vertex set of $T_1 \\times T_2$. This article studies dynamical systems associated with BM groups. A higher rank Cuntz-Krieger algebra $\\mathcal A(\\G)$ is associated both with a 2-dimensional tiling system and with a boundary action of a BM group $\\Gamma$. An explicit expression is given for the K-theory of $\\mathcal A(\\G)$. In particular $K_0=K_1$. A complete enumeration of possible BM groups $\\G$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5784","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"}