{"paper":{"title":"Singular multivalued homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Multivalued singular homology vanishes in all positive degrees for compact Hausdorff spaces.","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Alejandro O. Majadas-Moure","submitted_at":"2026-05-12T17:55:26Z","abstract_excerpt":"Let $X$ be a compact, Hausdorff topological space. Then $H^M_n(X)=0$ for all $n>0$, where $H_n$ is the multivalued analogue of singular homology. The case $n=1$ is already known [8]."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Let X be a compact, Hausdorff topological space. Then H^M_n(X)=0 for all n>0, where H_n is the multivalued analogue of singular homology.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The multivalued homology construction is well-defined on compact Hausdorff spaces and the topological properties of compactness and the Hausdorff axiom are sufficient to force vanishing in every positive degree.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Multivalued singular homology vanishes in all positive degrees for compact Hausdorff spaces.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Multivalued singular homology vanishes in all positive degrees for compact Hausdorff spaces.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b05fe9e195c21219629f6ee6f273ff817a96040e4abfdea62ec5ab1b6ced61a7"},"source":{"id":"2605.12585","kind":"arxiv","version":1},"verdict":{"id":"fa97e522-e288-4aa9-8717-954f6165b58d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:31:45.470682Z","strongest_claim":"Let X be a compact, Hausdorff topological space. Then H^M_n(X)=0 for all n>0, where H_n is the multivalued analogue of singular homology.","one_line_summary":"Multivalued singular homology vanishes in all positive degrees for compact Hausdorff spaces.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The multivalued homology construction is well-defined on compact Hausdorff spaces and the topological properties of compactness and the Hausdorff axiom are sufficient to force vanishing in every positive degree.","pith_extraction_headline":"Multivalued singular homology vanishes in all positive degrees for compact Hausdorff spaces."},"references":{"count":13,"sample":[{"doi":"","year":1971,"title":"Bourbaki (1971)","work_id":"2f340741-f418-45d4-bbb3-75f96508605e","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1946,"title":"S. Eilenberg, D. Montgomery (1946).Fixed point theorems for multivalued transfor- mations, Amer. J. Math.58, 214–222","work_id":"5eb975ec-27ab-44d3-8471-bbdd99643197","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"P. G. Goerss, J. F. Jardine (1999).Simplicial homotopy theory, Progress in Mathe- matics,174, 510 pp","work_id":"ab3eecc4-5b99-4d58-af60-2361c9f24992","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1977,"title":"Grothendieck et al.,S´ eminaire de G´ eom˜ netrie Alg´ ebrique, SGA5, Lecture Notes in Math.,589, Springer, 1977","work_id":"b4e415a5-eec4-4423-90ae-73454ed35ebb","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1941,"title":"Kakutani (1941).A generalization of Brouwer’s fixed point theorem, Duke Mat","work_id":"16c1386e-ab55-4433-9ab7-6eecdf96e28d","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":13,"snapshot_sha256":"af686f37181016818b6fef98fe6f433b843a9058efde9957af400e94c177ccee","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"568b7270ef9830fe06d72699bc32fd21135cba99223b166629deeb93e66a6d76"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}