{"paper":{"title":"Flat manifolds with holonomy group Z_2^k of diagonal type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Andrzej Szczepa\\'nski, Anna G\\k{a}sior","submitted_at":"2012-04-10T12:41:51Z","abstract_excerpt":"We consider relations between two families of flat manifolds with holonomy group (Z_2)^k of diagonal type. The family ${\\cal RBM}$ of real Bott manifolds and the family ${\\cal GHW}$ of generalized Hantzsche-Wendt manifolds. In particular, we prove that the intersection ${\\cal GHW}\\cap {\\cal RBM}$ is not empty. We also consider some class of real Bott manifolds without $\\operatorname{Spin}$ and $\\operatorname{Spin}^{\\C}$ structure. There are given conditions for the (non)existence of such structures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2127","kind":"arxiv","version":2},"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"}