{"paper":{"title":"Some remarks on the parametrized Borsuk-Ulam theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"India), Mahender Singh (IISER Mohali, Michael Crabb (University of Aberdeen, UK)","submitted_at":"2017-11-07T11:09:10Z","abstract_excerpt":"Given a locally trivial fibre bundle $E \\to B$ (with fibres and base finite complexes), an orthogonal real line bundle $\\lambda$ over $E$ and a real vector bundle $\\xi$ over $B$, we consider a fibrewise map $f : S(\\lambda ) \\to \\xi$ over $B$ defined on the unit sphere bundle of $\\lambda$. Following the fundamental work of Jaworowski and Dold on the parametrized Borsuk-Ulam theorem, we investigate lower bounds on the cohomological dimension of the set of points $v$ in $S(\\lambda )$ such that $f(v) = f(-v)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02397","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"}