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We prove that the cohomological dimension of SI(S_g) is g-1 when g > 0. We also show that H_g-1(SI(S_g);Z) is infinitely generated when g > 1. In particular, SI(S_3) is not finitely presentable. Finally, we apply our main results to show that the kernel of the Burau representation of the braid group B_n at t = -1 has cohomological dim"},"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":"1110.0448","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-03T19:23:25Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e7878b4f3478734564773c92b6727b4745719570fdaa1d64073b3887bfecf8a5","abstract_canon_sha256":"b858038845998e664f219cff8f0cf99418d0b684860a8d18ff54c82c4ad9d6dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:49.912474Z","signature_b64":"zVl52nRyp9ZsVUc36Xi+k5efF3U+YK7jGbb8VUt4yzUI6tldom0D/MoBku49mKX3MEVeGD4r4IbVvthItkTyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62802a2f8b983e8883d211d4043480cbbdbddfd45911a182b5f7c424025436b7","last_reissued_at":"2026-05-18T04:11:49.911698Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:49.911698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cohomology of the hyperelliptic Torelli group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GT","authors_text":"Dan Margalit, Leah Childers, Tara Brendle","submitted_at":"2011-10-03T19:23:25Z","abstract_excerpt":"Let SI(S_g) denote the hyperelliptic Torelli group of a closed surface S_g of genus g. This is the subgroup of the mapping class group of S_g consisting of elements that act trivially on H_1(S_g;Z) and that commute with some fixed hyperelliptic involution of S_g. We prove that the cohomological dimension of SI(S_g) is g-1 when g > 0. We also show that H_g-1(SI(S_g);Z) is infinitely generated when g > 1. In particular, SI(S_3) is not finitely presentable. Finally, we apply our main results to show that the kernel of the Burau representation of the braid group B_n at t = -1 has cohomological dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0448","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1110.0448","created_at":"2026-05-18T04:11:49.911851+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.0448v1","created_at":"2026-05-18T04:11:49.911851+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0448","created_at":"2026-05-18T04:11:49.911851+00:00"},{"alias_kind":"pith_short_12","alias_value":"MKACUL4LTA7I","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"MKACUL4LTA7IRA6S","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"MKACUL4L","created_at":"2026-05-18T12:26:34.985390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MKACUL4LTA7IRA6SCHKAINEAZO","json":"https://pith.science/pith/MKACUL4LTA7IRA6SCHKAINEAZO.json","graph_json":"https://pith.science/api/pith-number/MKACUL4LTA7IRA6SCHKAINEAZO/graph.json","events_json":"https://pith.science/api/pith-number/MKACUL4LTA7IRA6SCHKAINEAZO/events.json","paper":"https://pith.science/paper/MKACUL4L"},"agent_actions":{"view_html":"https://pith.science/pith/MKACUL4LTA7IRA6SCHKAINEAZO","download_json":"https://pith.science/pith/MKACUL4LTA7IRA6SCHKAINEAZO.json","view_paper":"https://pith.science/paper/MKACUL4L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.0448&json=true","fetch_graph":"https://pith.science/api/pith-number/MKACUL4LTA7IRA6SCHKAINEAZO/graph.json","fetch_events":"https://pith.science/api/pith-number/MKACUL4LTA7IRA6SCHKAINEAZO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MKACUL4LTA7IRA6SCHKAINEAZO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MKACUL4LTA7IRA6SCHKAINEAZO/action/storage_attestation","attest_author":"https://pith.science/pith/MKACUL4LTA7IRA6SCHKAINEAZO/action/author_attestation","sign_citation":"https://pith.science/pith/MKACUL4LTA7IRA6SCHKAINEAZO/action/citation_signature","submit_replication":"https://pith.science/pith/MKACUL4LTA7IRA6SCHKAINEAZO/action/replication_record"}},"created_at":"2026-05-18T04:11:49.911851+00:00","updated_at":"2026-05-18T04:11:49.911851+00:00"}