{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WNSPA3YVDGF3VG4Q7HRYYITOQB","short_pith_number":"pith:WNSPA3YV","schema_version":"1.0","canonical_sha256":"b364f06f15198bba9b90f9e38c226e805007305960300b72a54796815b18891f","source":{"kind":"arxiv","id":"1310.6212","version":1},"attestation_state":"computed","paper":{"title":"Some Computations in Equivariant cobordism in relation to Milnor manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Goutam Mukherjee, Samik Basu, Swagata Sarkar","submitted_at":"2013-10-23T13:06:27Z","abstract_excerpt":"Let $\\mathcal{N}_*$ be the unoriented cobordism algebra, let $G=(\\Z_2)^n$ and let $Z_*(G)$ denote the equivariant cobordism algebra of $G$-manifolds with finite stationary point sets. Let $\\epsilon_* :Z_*(G) \\to \\mathcal{N}_*$ be the homomorphism which forgets the $G$-action. We use Milnor manifolds (degree 1 hypersurfaces in $\\R P^m\\times \\R P^n$) to construct non-trivial elements in $Z_*(G)$. We prove that these elements give rise to indecomposable elements in $Z_*(G)$ in degrees up to $2^n - 5$. Moreover, in most cases these elements can be arranged to be in $\\mathit{Ker}(\\epsilon_*)$."},"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":"1310.6212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-10-23T13:06:27Z","cross_cats_sorted":[],"title_canon_sha256":"4b5cdfd15e5de7b0676afec6655520ba167e873c35011723cf9cb174b605a286","abstract_canon_sha256":"3e25809320989e17ae3c5eec1ae9f164092f948730053e2ed097df590688f159"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:21.025644Z","signature_b64":"rktuJf2x7qtfFMF2uNEwr0ayc2geNQTz6F1tRB0XwHG9hJp7u2ytxn0NcWlrKTkuwxa/EO6nllOdq/A2P81MAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b364f06f15198bba9b90f9e38c226e805007305960300b72a54796815b18891f","last_reissued_at":"2026-05-18T03:09:21.024788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:21.024788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Computations in Equivariant cobordism in relation to Milnor manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Goutam Mukherjee, Samik Basu, Swagata Sarkar","submitted_at":"2013-10-23T13:06:27Z","abstract_excerpt":"Let $\\mathcal{N}_*$ be the unoriented cobordism algebra, let $G=(\\Z_2)^n$ and let $Z_*(G)$ denote the equivariant cobordism algebra of $G$-manifolds with finite stationary point sets. Let $\\epsilon_* :Z_*(G) \\to \\mathcal{N}_*$ be the homomorphism which forgets the $G$-action. We use Milnor manifolds (degree 1 hypersurfaces in $\\R P^m\\times \\R P^n$) to construct non-trivial elements in $Z_*(G)$. We prove that these elements give rise to indecomposable elements in $Z_*(G)$ in degrees up to $2^n - 5$. Moreover, in most cases these elements can be arranged to be in $\\mathit{Ker}(\\epsilon_*)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6212","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":"1310.6212","created_at":"2026-05-18T03:09:21.024943+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.6212v1","created_at":"2026-05-18T03:09:21.024943+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6212","created_at":"2026-05-18T03:09:21.024943+00:00"},{"alias_kind":"pith_short_12","alias_value":"WNSPA3YVDGF3","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"WNSPA3YVDGF3VG4Q","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"WNSPA3YV","created_at":"2026-05-18T12:28:04.890932+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/WNSPA3YVDGF3VG4Q7HRYYITOQB","json":"https://pith.science/pith/WNSPA3YVDGF3VG4Q7HRYYITOQB.json","graph_json":"https://pith.science/api/pith-number/WNSPA3YVDGF3VG4Q7HRYYITOQB/graph.json","events_json":"https://pith.science/api/pith-number/WNSPA3YVDGF3VG4Q7HRYYITOQB/events.json","paper":"https://pith.science/paper/WNSPA3YV"},"agent_actions":{"view_html":"https://pith.science/pith/WNSPA3YVDGF3VG4Q7HRYYITOQB","download_json":"https://pith.science/pith/WNSPA3YVDGF3VG4Q7HRYYITOQB.json","view_paper":"https://pith.science/paper/WNSPA3YV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.6212&json=true","fetch_graph":"https://pith.science/api/pith-number/WNSPA3YVDGF3VG4Q7HRYYITOQB/graph.json","fetch_events":"https://pith.science/api/pith-number/WNSPA3YVDGF3VG4Q7HRYYITOQB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WNSPA3YVDGF3VG4Q7HRYYITOQB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WNSPA3YVDGF3VG4Q7HRYYITOQB/action/storage_attestation","attest_author":"https://pith.science/pith/WNSPA3YVDGF3VG4Q7HRYYITOQB/action/author_attestation","sign_citation":"https://pith.science/pith/WNSPA3YVDGF3VG4Q7HRYYITOQB/action/citation_signature","submit_replication":"https://pith.science/pith/WNSPA3YVDGF3VG4Q7HRYYITOQB/action/replication_record"}},"created_at":"2026-05-18T03:09:21.024943+00:00","updated_at":"2026-05-18T03:09:21.024943+00:00"}