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It is easy to see that the reflections in the points q_1,q_2 obtained from p_1,p_2 by moving p_1,p_2 along the geodesic generated by p_1,p_2 and keeping the (dis)tance between p_1,p_2 satisfy the bending relation R(q_2)R(q_1)=R(p_2)R(p_1). We show that a generic isometry F\\in SU(2,1) is a product of 3 reflections, F=R(p_3)R(p_2)R(p_1), and describe all such decompositions: two decompositions are connected by finitely many bendings involving p_1,p_2/p_2,p_3 and geometrically equal decomposit"},"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":"1201.1582","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-07T20:14:20Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"6fcc1992c5c1ba4fa0e15c87e336fbba3c36da30341fd4519c755a6598b8a930","abstract_canon_sha256":"7cb3558f5c7c33effe7c2a80b0b7a70bb6dc02540465352dcbedcc91586eae69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:54.430454Z","signature_b64":"j36j/JpNfJoG0qxuCMYxyoeOsfATD53lelJjYD6yXAxS+luc3zrYtVrlrMt+6wVVsAr8FuwowhZRxRCj6CDiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"079810f110c19eca3b46c5c3b6bae5de6d059c2bee0068bd3e67aa516db7eac6","last_reissued_at":"2026-05-18T04:04:54.429857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:54.429857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reflections, bendings, and pentagons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"Sasha Anan'in","submitted_at":"2012-01-07T20:14:20Z","abstract_excerpt":"We study relations between reflections in (positive or negative) points in the complex hyperbolic plane. 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