{"paper":{"title":"On the second nilpotent quotient of higher homotopy groups, for hypersolvable arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Daniela Anca Macinic, Daniel Matei, Stefan Papadima","submitted_at":"2013-02-23T16:18:51Z","abstract_excerpt":"We examine the first non-vanishing higher homotopy group, $\\pi_p$, of the complement of a hypersolvable, non--supersolvable, complex hyperplane arrangement, as a module over the group ring of the fundamental group, $\\Z\\pi_1$. We give a presentation for the $I$--adic completion of $\\pi_p$. We deduce that the second nilpotent $I$--adic quotient of $\\pi_p$ is determined by the combinatorics of the arrangement, and we give a combinatorial formula for the second associated graded piece, $\\gr^1_I \\pi_p$. We relate the torsion of this graded piece to the dimensions of the minimal generating systems o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5822","kind":"arxiv","version":2},"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"}