{"paper":{"title":"Smooth manifolds homotopy equivalent to products of spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Sagnik Biswas","submitted_at":"2026-06-08T22:58:55Z","abstract_excerpt":"We classify, up to almost diffeomorphism, the smooth closed oriented manifolds homotopy equivalent to each of the sphere products $S^{4k-1}\\times S^{4k}$, $S^{4k}\\times S^{4k}$, and $S^{4k}\\times S^{4k+1}$. In each case we realize the image of the normal-invariant map in the smooth surgery exact sequence by explicit families of manifolds: sphere bundles over $S^{4k}$; pinch maps and Milnor plumbings of disk bundles; and Novikov sphere bundles together with connected sums of homotopy spheres."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10239","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/2606.10239/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"}