{"paper":{"title":"Spaces of sections of Banach algebra bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.OA","authors_text":"Claude L. Schochet, Emmanuel Dror Farjoun","submitted_at":"2011-01-03T01:52:53Z","abstract_excerpt":"Suppose that $B$ is a $G$-Banach algebra over $\\mathbb{F} = \\mathbb{R}$ or $\\mathbb{C}$, $X$ is a finite dimensional compact metric space, $\\zeta : P \\to X$ is a standard principal $G$-bundle, and $A_\\zeta = \\Gamma (X, P \\times_G B)$ is the associated algebra of sections.\n  We produce a spectral sequence which converges to $\\pi_*(GL_o A_\\zeta) $ with [E^2_{-p,q} \\cong \\check{H}^p(X ; \\pi_q(GL_o B)).] A related spectral sequence converging to $\\K_{*+1}(A_\\zeta)$ (the real or complex topological $K$-theory) allows us to conclude that if $B$ is Bott-stable, (i.e., if $ \\pi_*(GL_o B) \\to \\K_{*+1}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0444","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"}