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The main results are as follows.\n  (1) Under the assumption that $e_{\\ast}$ is isomorphic for $q^{-1}(F)$ for any finite subgroup $F$ of $\\Gamma/N$, we prove that $e_{\\ast}$ is injective, surjective and isomorphic for $\\Gamma$ if they are also true for $\\Gamma/N$, respec"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2601.09615","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-01-14T16:37:20Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"ec8efc3363b089af0f1cc3f5957f893cce29f69cf7539759d45387d201efe982","abstract_canon_sha256":"1241dd6416e330b4a2d9feeb933f555932040b5c6d98a521a21eb70dfd9cb117"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:14.647896Z","signature_b64":"DIKEvbGkhQTGumu/8OBOGiLdjm0YA7FN1iu42Q3Y/wqej1GRpM7cxBoOuafgTaa2vffB8M7+HhrqDg/WKCQgAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baebdc545bb8555b7e842f91030b1c9409a80dfeed3924f7a16a110aaa042284","last_reissued_at":"2026-06-30T02:17:14.647309Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:14.647309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Baum-Connes and the Mishchenko-Kasparov assembly maps for group extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Jianguo Zhang","submitted_at":"2026-01-14T16:37:20Z","abstract_excerpt":"In this paper, we investigate the injectivity, surjectivity and isomorphism of the Baum--Connes assembly map $e_{\\ast}$ with coefficients, and the injectivity of the Mishchenko--Kasparov assembly map $\\mu_{\\ast}$ with coefficients for group extensions $1\\rightarrow N \\rightarrow \\Gamma \\xrightarrow{q} \\Gamma/ N \\rightarrow 1$. 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