{"paper":{"title":"Euler characteristics and Gysin sequences for group actions on boundaries","license":"","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Heath Emerson, Ralf Meyer","submitted_at":"2005-05-03T09:37:30Z","abstract_excerpt":"Let G be a locally compact group, let X be a universal proper G-space, and let Z be a G-equivariant compactification of X that is H-equivariantly contractible for each compact subgroup H of G. Let W be the resulting boundary. Assuming the Baum-Connes conjecture for G with coefficients C and C(W), we construct an exact sequence that computes the map on K-theory induced by the embedding of the reduced group C*-algebra of G into the crossed product of G by C(W). This exact sequence involves the equivariant Euler characteristic of X, which we study using an abstract notion of Poincare duality in b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505050","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"}