{"paper":{"title":"The K(\\pi, 1) problem for the affine Artin group of type \\widetilde{B}_n and its cohomology","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Davide Moroni, Filippo Callegaro, Mario Salvetti","submitted_at":"2007-05-19T17:26:33Z","abstract_excerpt":"In this paper we prove that the complement to the affine complex arrangement of type \\widetilde{B}_n is a K(\\pi, 1) space. We also compute the cohomology of the affine Artin group G of type \\widetilde{B}_n with coefficients over several interesting local systems. In particular, we consider the module Q[q^{\\pm 1}, t^{\\pm 1}], where the first n-standard generators of G act by (-q)-multiplication while the last generator acts by (-t)-multiplication. Such representation generalizes the analog 1-parameter representation related to the bundle structure over the complement to the discriminant hypersu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.2830","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"}