{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T18:11:40Z","timestamp":1676657500400},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,11]]},"abstract":"<jats:p>An [Formula: see text]-dimensional closed flat manifold is said to be of diagonal type if the standard representation of its holonomy group [Formula: see text] is diagonal. An [Formula: see text]-dimensional Bieberbach group of diagonal type is the fundamental group of such a manifold. We introduce the diagonal Vasquez invariant of [Formula: see text] as the least integer [Formula: see text] such that every flat manifold of diagonal type with holonomy [Formula: see text] fibers over a flat manifold of dimension at most [Formula: see text] with flat torus fibers. Using a combinatorial description of Bieberbach groups of diagonal type, we give both upper and lower bounds for this invariant. We show that the lower bounds are exact when [Formula: see text] has low rank. We apply this to analyze diffuseness properties of Bieberbach groups of diagonal type. This leads to a complete classification of Bieberbach groups of diagonal type with Klein four-group holonomy and to an application to Kaplansky\u2019s Unit Conjecture.<\/jats:p>","DOI":"10.1142\/s0218196722500631","type":"journal-article","created":{"date-parts":[[2022,8,31]],"date-time":"2022-08-31T08:36:55Z","timestamp":1661935015000},"page":"1411-1445","source":"Crossref","is-referenced-by-count":0,"title":["Fibering flat manifolds of diagonal type and their fundamental groups"],"prefix":"10.1142","volume":"32","author":[{"given":"Ho Yiu","family":"Chung","sequence":"first","affiliation":[{"name":"School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK"}]},{"given":"Nansen","family":"Petrosyan","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK"}]}],"member":"219","published-online":{"date-parts":[[2022,9,30]]},"reference":[{"key":"S0218196722500631BIB001","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610700001307"},{"key":"S0218196722500631BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8687-2"},{"key":"S0218196722500631BIB004","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1090\/conm\/093\/1003347","volume":"93","author":"Cliff G.","year":"1989","journal-title":"Contemp. 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