{"paper":{"title":"Restricting cohomology classes to disk and segment configuration spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.MG","authors_text":"Hannah Alpert","submitted_at":"2016-08-23T19:31:11Z","abstract_excerpt":"The configuration space of n labeled disks of radius r inside the unit disk is denoted Conf_{n, r}(D^2). We study how the cohomology of this space depends on r. In particular, given a cohomology class of Conf_{n, 0}(D^2), for which r does its restriction to Conf_{n, r}(D^2) vanish? A related question: given the configuration space Seg_{n, r}(D^2) of n labeled, oriented segments of length r, it has a map to (S^1)^n that records the direction of each segment. For which r does this angle map have a continuous section? The paper consists of a collection of partial results, and it contains many que"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06612","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"}