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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2311.13477","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-11-22T15:48:10Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"dbe0e533992bfe852ab95dc2c24a29542d92453324bb4cbf9a779876b07bd732","abstract_canon_sha256":"7d107de416d6cced5958a33651cb6a40dd395b242f84505c0c2a3332e9ff5c09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:15:38.794394Z","signature_b64":"xV0iS+2cgrXbWzuJNnxiHldFPQFQe1zOAum2FKl/CftjpxfVBBtXt9TQroPZv5mO9faynEMogIZGvNV+QqM4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3fb512bb9890a9e7600206446fe8b1a0da067096d89a8cbcc8c16da5d35c33b","last_reissued_at":"2026-07-05T07:15:38.793794Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:15:38.793794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $k \\leq2(r-1)(g-1)-1$. 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