{"paper":{"title":"Foliation-preserving Maps Between Solvmanifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Dave Witte, Holly Bernstein","submitted_at":"1998-02-10T00:00:00Z","abstract_excerpt":"For i = 1,2, let Gamma_i be a lattice in a simply connected, solvable Lie group G_i, and let X_i be a connected Lie subgroup of G_i. The double cosets Gamma_igX_i provide a foliation F_i of the homogeneous space Gamma_i\\G_i. Let f be a continuous map from Gamma_1\\G_1 to Gamma_2\\G_2 whose restriction to each leaf of F_1 is a covering map onto a leaf of F_2. If we assume that F_1 has a dense leaf, and make certain technical technical assumptions on the lattices Gamma_1 and Gamma_2, then we show that f must be a composition of maps of two basic types: a homeomorphism of Gamma_1\\M_1 that takes eac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9802133","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"}