{"paper":{"title":"Parametrized Borsuk-Ulam problem for projective space bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Mahender Singh","submitted_at":"2008-10-26T07:41:53Z","abstract_excerpt":"Let $\\pi: E \\to B$ be a fiber bundle with fiber having the mod 2 cohomology algebra of a real or a complex projective space and let $\\pi^{'}: E^{'} \\to B$ be vector bundle such that $\\mathbb{Z}_2$ acts fiber preserving and freely on $E$ and $E^{'}-0$, where 0 stands for the zero section of the bundle $\\pi^{'}:E^{'} \\to B$. For a fiber preserving $\\mathbb{Z}_2$-equivariant map $f:E \\to E^{'}$, we estimate the cohomological dimension of the zero set $Z_f = \\{x \\in E | f(x)= 0\\}.$ As an application, we also estimate the cohomological dimension of the $\\mathbb{Z}_2$-coincidence set $A_f=\\{x \\in E "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.4669","kind":"arxiv","version":3},"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"}