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Our main results may be summarised as follows: first, the pure braid group short exact sequence\n  1 --> P_{m-n}(RP^2 - {x_1,...,x_n}) --> P_m(RP^2) --> P_n(RP^2) --> 1\n does not split if m > 3 and n=2,3. Now let n > 1. Then in B_n(RP^2), there is a k-torsion "},"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":"math/0409350","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2004-09-20T13:08:54Z","cross_cats_sorted":[],"title_canon_sha256":"2bb5121b6e358d4eb828ba298827ffef9428b72162daf0ff0c85ac94b28c0bc2","abstract_canon_sha256":"0d64d989431531b10c895ad494a1c8baba4870d78fef86159bf63e9e92e5f6ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:32.303361Z","signature_b64":"cuFmgmOsnFVWbrbuNpQF+fYrZk2Je1tsJtVu1YgBnu9DzsRle6DihXyhnApooARN5zYT6t6EIyt0hc7i5eOJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"985d637eb9b72e01ac8777e47486778fb98917664487bb63f3a12c71418a50d6","last_reissued_at":"2026-05-18T02:41:32.302964Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:32.302964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The braid groups of the projective plane","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Daciberg Lima Goncalves, John Guaschi","submitted_at":"2004-09-20T13:08:54Z","abstract_excerpt":"Let B_n(RP^2)$ (respectively P_n(RP^2)) denote the braid group (respectively pure braid group) on n strings of the real projective plane RP^2. In this paper we study these braid groups, in particular the associated pure braid group short exact sequence of Fadell and Neuwirth, their torsion elements and the roots of the `full twist' braid. Our main results may be summarised as follows: first, the pure braid group short exact sequence\n  1 --> P_{m-n}(RP^2 - {x_1,...,x_n}) --> P_m(RP^2) --> P_n(RP^2) --> 1\n does not split if m > 3 and n=2,3. Now let n > 1. 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