{"paper":{"title":"On the cohomology of the mapping class group of the punctured projective plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Miguel A. Maldonado, Miguel A. Xicot\\'encatl","submitted_at":"2017-05-22T18:26:30Z","abstract_excerpt":"The mapping class group $\\Gamma^k(N_g)$ of a non-orientable surface with punctures is studied via classical homotopy theory of configuration spaces. In particular, we obtain a non-orientable version of the Birman exact sequence. In the case of $\\mathbb R {\\rm P}^2$, we analize the Serre spectral sequence of a fiber bundle $F_k(\\mathbb R {\\rm P}^2)/\\Sigma_k \\to X_k \\to BSO(3)$ where $X_k$ is a $K(\\Gamma^k(\\mathbb R {\\rm P}^2),1)$ and $F_k(\\mathbb R {\\rm P}^2)/\\Sigma_k$ denotes the configuration space of unordered $k$-tuples of distinct points in $\\mathbb R {\\rm P}^2$. As a consequence, we expre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07937","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"}