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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The classification of flat solvmanifolds


Author: Alexander Morgan
Journal: Trans. Amer. Math. Soc. 239 (1978), 321-351
MSC: Primary 22E25
MathSciNet review: 0470138
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Abstract: This paper contains a complete algebraic characterization of the fundamental groups of flat solvmanifolds. This characterization is in terms of finite integral representations of free abelian groups and the associated cohomology. A classification of compact flat solvmanifolds follows, and a list of all compact flat solvmanifolds of dimensions 3, 4, and 5 (except the 5-dimensional with first betti number 1) is given.

Some theorems on the classification of noncompact flat solvmanifolds have also been obtained. These give full results in some cases, partial results in others. For example, the odd order holonomy group case is completely settled.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0470138-4
PII: S 0002-9947(1978)0470138-4
Keywords: Flat manifold, solvmanifold, finite integral representation
Article copyright: © Copyright 1978 American Mathematical Society