{"paper":{"title":"Topology of moduli of parabolic connections with fixed determinant","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Nilkantha Das, Sumit Roy","submitted_at":"2023-11-22T15:48:10Z","abstract_excerpt":"Let $X$ be a compact Riemann surface of genus $g \\geq 2$ and $D\\subset X$ be a fixed finite subset. Let $\\xi$ be a line bundle of degree $d$ over $X$. Let $\\mathcal{M}(\\alpha, r, \\xi)$ (respectively, $\\mathcal{M}_{\\mathrm{conn}}(\\alpha, r, \\xi)$) denote the moduli space of stable parabolic bundles (respectively, parabolic connections) of rank $r$ $(\\geq 2)$, determinant $\\xi$ and full flag generic rational parabolic weight type $\\alpha$. We show that $\n  \\pi_k(\\mathcal{M}_{\\mathrm{conn}}(\\alpha, r, \\xi)) \\cong \\pi_k(\\mathcal{M}(\\alpha, r, \\xi)) $ for $k \\leq2(r-1)(g-1)-1$. As a consequence, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.13477","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/2311.13477/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"}