{"paper":{"title":"The structure theory of Nilspaces I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GN"],"primary_cat":"math.DS","authors_text":"Freddie Manners, P\\'eter P. Varj\\'u, Yonatan Gutman","submitted_at":"2016-05-28T22:57:40Z","abstract_excerpt":"This paper forms the first part of a series by the authors [GMV2,GMV3] concerning the structure theory of nilspaces of Antol\\'in Camarena and Szegedy. A nilspace is a compact space $X$ together with closed collections of cubes $C^n(X)\\subseteq X^{2^n}$, $n=1,2,\\ldots$ satisfying some natural axioms. Antol\\'in Camarena and Szegedy proved that from these axioms it follows that (certain) nilspaces are isomorphic (in a strong sense) to an inverse limit of nilmanifolds. The aim of our project is to provide a new self-contained treatment of this theory and give new applications to topological dynami"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08945","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"}