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Two HW-manifolds M_1 and M_2 are cohomological rigid if and only if a homeomorphism between M_1 and M_2 is equivalent to an isomorphism of graded rings H^{*}(M_1,F_2) and H^{*}(M_2,F_2). We prove that HW-manifolds are cohomological rigid."},"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":"1303.2807","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-03-12T08:43:24Z","cross_cats_sorted":[],"title_canon_sha256":"ac861fba54ade392de032419ab1c746e6b3ef5f11345b24c49c415380e8786cd","abstract_canon_sha256":"fa9468bdb463fdebf70d8c3ebace57fc583d611926d14504deed599ea7c8ff6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:12.258072Z","signature_b64":"hxIjzWz+slxTEXN7OH46v5y3WDXLQm2bQchu9LEiYQo6nL5x85eks+S8f8htyvG6wQYliiNz411UGcpNjz2HAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10202cd35160c523bb28bd031cdfa027ef4e0a872ce099cf8f652ce743070ecb","last_reissued_at":"2026-05-18T01:03:12.257562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:12.257562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cohomological rigidity of oriented Hantzsche-Wendt manidolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Andrzej Szczepanski, Jerzy Popko","submitted_at":"2013-03-12T08:43:24Z","abstract_excerpt":"By Hantzsche-Wendt manifold (for short HW-manifold) we understand any oriented closed Riemannian manifold of dimension n with a holonomy group (Z_2)^{n-1}. Two HW-manifolds M_1 and M_2 are cohomological rigid if and only if a homeomorphism between M_1 and M_2 is equivalent to an isomorphism of graded rings H^{*}(M_1,F_2) and H^{*}(M_2,F_2). 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