{"paper":{"title":"On the Homology of Configuration Spaces Associated to Centers of Mass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Dai Tamaki","submitted_at":"2010-04-01T02:03:50Z","abstract_excerpt":"The aim of this paper is to make sample computations with the Salvetti complex of the \"center of mass\" arrangement introduced in [arXiv:math/0611732] by Cohen and Kamiyama. We compute the homology of the Salvetti complex of these arrangements with coefficients in the sign representation of symmetric groups on F_p in the case of four particles. We show, when p is an odd prime, the homology is isomorphic to the homology of the configuration space F(C,4) of distinct four points in the complex plane  with the same coefficients. When p=2, we show the homology is different from that of F(C,4), hence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0039","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"}