{"paper":{"title":"The path space of a higher-rank graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Samuel B. G. Webster","submitted_at":"2011-02-07T04:07:29Z","abstract_excerpt":"We construct a locally compact Hausdorff topology on the path space of a finitely aligned $k$-graph $\\Lambda$. We identify the boundary-path space $\\partial\\Lambda$ as the spectrum of a commutative $C^*$-subalgebra $D_\\Lambda$ of $C^*(\\Lambda)$. Then, using a construction similar to that of Farthing, we construct a finitely aligned $k$-graph $\\wt\\Lambda$ with no sources in which $\\Lambda$ is embedded, and show that $\\partial\\Lambda$ is homeomorphic to a subset of $\\partial\\wt\\Lambda$ . We show that when $\\Lambda$ is row-finite, we can identify $C^*(\\Lambda)$ with a full corner of $C^*(\\wt\\Lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1229","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"}