{"paper":{"title":"Augmental Homology and the Kynneth Formula for Joins","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"G. Fors","submitted_at":"2001-09-11T20:42:59Z","abstract_excerpt":"The \"simplicial complexes\" and \"join\" (*) today used within combinatorics aren't the classical concepts, cf. Spanier (1966) p. 108-9, but, exept for \\emptyset, complexes having {\\emptyset} as a subcomplex resp. \\Sigma1 * \\Sigma2 := {\\sigma1 \\cup \\sigma2 | \\sigmai \\in \\Sigmai} implying a tacit change of unit element w.r.t. the join operation, from \\emptyset to {\\emptyset}. Extending the classical realization functor to this category of simplicial complexes we end up with a \"restricted\" category of topological spaces, \"containing\" the classical and where the classical (co)homology theory, as wel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0109073","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0109073/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}