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In this paper, we extend this property to arrangements whose graphs are a disjoint union of cycle-tree graphs.\n  Moreover, we"},"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":"1009.1349","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-09-07T17:34:52Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"b88cc3d476562195cdb61f38f38200258b961763e0ad93ede49e0856ffa895c1","abstract_canon_sha256":"8cd36e276ef1f380f541e1e47891f6adae93603d2d6259380a412e2999e70468"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:06.284421Z","signature_b64":"YI2lqjwWscsvZF5h6sFHQSAHLcEac2U+RK7Wx2TuuRTtHWZSrNhpa/WgGaVgrCYEqsj+y8cd+2VRmVBBwRUyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65356ef7bbdd9e8e201d2772786c09ad5c9a5262ace72b4d1663b9b7b9b4c24a","last_reissued_at":"2026-05-18T03:54:06.283883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:06.283883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A conjugation-free geometric presentation of fundamental groups of arrangements II: Expansion and some properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.GT","authors_text":"David Garber, Meital Eliyahu, Mina Teicher","submitted_at":"2010-09-07T17:34:52Z","abstract_excerpt":"A conjugation-free geometric presentation of a fundamental group is a presentation with the natural topological generators $x_1, ..., x_n$ and the cyclic relations: $x_{i_k}x_{i_{k-1}} ... x_{i_1} = x_{i_{k-1}} ... x_{i_1} x_{i_k} = ... = x_{i_1} x_{i_k} ... x_{i_2}$ with no conjugations on the generators.\n  We have already proved that if the graph of the arrangement is a disjoint union of cycles, then its fundamental group has a conjugation-free geometric presentation. 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