{"paper":{"title":"Automorphism groups of rigid geometries on leaf spaces of foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Nina I. Zhukova","submitted_at":"2017-04-13T17:39:30Z","abstract_excerpt":"We introduce a category of rigid geometries on singular spaces which are leaf spaces of foliations and are considered as leaf manifolds. We single out a special category $\\mathfrak F_0$ of leaf manifolds containing the orbifold category as a full subcategory. Objects of $\\mathfrak F_0$ may have non-Hausdorff topology unlike the orbifolds. The topology of some objects of $\\mathfrak F_0$ does not satisfy the separation axiom $T_0$. It is shown that for every ${\\mathcal N}\\in Ob(\\mathfrak F_0)$ a rigid geometry $\\zeta$ on $\\mathcal N$ admits a desingularization. Moreover, for every such $\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04220","kind":"arxiv","version":3},"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"}