{"paper":{"title":"K-theory of crossed products of tiling C*-algebras by rotation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Charles Starling","submitted_at":"2013-10-21T13:59:11Z","abstract_excerpt":"Let $\\Omega$ be a tiling space and let $G$ be the maximal group of rotations which fixes $\\Omega$. Then the cohomology of $\\Omega$ and $\\Omega/G$ are both invariants which give useful geometric information about the tilings in $\\Omega$. The noncommutative analog of the cohomology of $\\Omega$ is the K-theory of a C*-algebra associated to $\\Omega$, and for translationally finite tilings of dimension 2 or less the K-theory is isomorphic to the direct sum of cohomology groups. In this paper we give a prescription for calculating the noncommutative analog of the cohomology of $\\Omega/G$, that is, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5549","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"}