{"paper":{"title":"Non-orientable surfaces in homology cobordisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Adam Simon Levine, Daniel Ruberman, Ira M. Gessel, Saso Strle","submitted_at":"2013-10-31T14:21:49Z","abstract_excerpt":"We investigate constraints on embeddings of a non-orientable surface in a $4$-manifold with the homology of $M \\times I$, where $M$ is a rational homology $3$-sphere. The constraints take the form of inequalities involving the genus and normal Euler class of the surface, and either the Ozsv\\'ath--Sazb\\'o $d$-invariants or Atiyah--Singer $\\rho$-invariants of $M$. One consequence is that the minimal genus of a smoothly embedded surface in $L(2p,q) \\times I$ is the same as the minimal genus of a surface in $L(2p,q)$. We also consider embeddings of non-orientable surfaces in closed $4$-manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8516","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"}