Compact flat manifolds with holonomy group \(\mathbb Z_2\oplus\mathbb Z_2\). II
type: Item
instance of: scholarly article
title: Compact flat manifolds with holonomy group \(\mathbb Z_2\oplus\mathbb Z_2\). II
zbMATH Open document ID: 0970.53029
author: P. A. Tirao
author: Juan Pablo Rossetti
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2001-10-14T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108496
review text: The classification of compact flat manifolds (up to affine equivalence) is equivalent, after Bieberbach's results, to the classification of their fundamental groups (up to isomorphism). In this paper the authors give a complete classification of compact flat manifolds with holonomy group \({\mathbb Z}_2\oplus{\mathbb Z}_2\), with the property that the holonomy representation is a direct sum of \({\mathbb Z}_2\oplus{\mathbb Z}_2\)-indecomposable representations of \({\mathbb Z}\)-rank equal to 1 or 2. The compact flat manifolds in this class which have first Betti number zero are exactly those considered in [the authors, Proc. Am. Math. Soc. 124, No. 8, 2491--2499 (1996; Zbl 0864.53027)].
reviewed by: Pascual Lucas Saorín
Mathematics Subject Classification ID: 53C29
Mathematics Subject Classification ID: 57S30
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 1319597
zbMATH Keywords: fundamental group
zbMATH Keywords: compact flat manifold
zbMATH Keywords: holonomy group
zbMATH Keywords: Betti number
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1319597