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For a representable ring cohomology theory A(-) with a special linear orientation and invertible stable Hopf map \\eta, including Witt groups and MSL[\\eta^{-1}], we have A(SGr(2,2n+1))=A(pt)[e]/(e^{2n}), and A(SGr(2,2n)) is a truncated polynomial algebra in two variables over A(pt). A splitting principle for such theories is established. We use the computations for the special linear Grassmann varieties to calculate A(BSL_n) in terms of the homogen"},"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":"1205.6067","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-28T09:51:46Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"c0aeacbfaf67b975a72f0117de5b77108ce69ff81d067016779e854a6eb3819e","abstract_canon_sha256":"ceba05fc27bc843e80271b94a5a6d376a20aadad5f2aaf6f5dcdfd5344e5ed82"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:18.697895Z","signature_b64":"wkynk1XZVJRrdwvAocPxm1CPzX1VSszvPBmA0sJISX4up6PHMFVhsExeJQ1LDiIgO3h+1hWzFJTGitjX3ogrBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe8235e4cd3995ffbf2b6705229e7a67e5a98b0c63922e82fb121ef49088f3eb","last_reissued_at":"2026-05-17T23:53:18.697351Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:18.697351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The special linear version of the projective bundle theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Alexey Ananyevskiy","submitted_at":"2012-05-28T09:51:46Z","abstract_excerpt":"A special linear Grassmann variety SGr(k,n) is the complement to the zero section of the determinant of the tautological vector bundle over Gr(k,n). 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