{"paper":{"title":"Torsion in Boundary Coinvariants and K-theory for Affine Buildings","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"Guyan Robertson","submitted_at":"2005-01-20T17:51:04Z","abstract_excerpt":"Let $(G,{\\mathfrak I},N,S)$ be an affine topological Tits system, and let $\\Gamma$ be a torsion free cocompact lattice in $G$. This article studies the coinvariants $H_0(\\Gamma; C(\\Omega,{\\mathbb Z}))$, where $\\Omega$ is the Furstenberg boundary of $G$. It is shown that the class $[1]$ of the identity function in $H_0(\\Gamma; C(\\Omega,{\\mathbb Z}))$ has finite order, with explicit bounds for the order.\n  A similar statement applies to the $K_0$ group of the boundary crossed product $C^*$-algebra $C(\\Omega)\\rtimes\\Gamma$. If the Tits system has type $\\widetilde A_2$, exact computations are give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501330","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"}