The classification of flat solvmanifolds

Morgan, Alexander

doi:10.1090/S0002-9947-1978-0470138-4

The classification of flat solvmanifolds
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Trans. Amer. Math. Soc. 239 (1978), 321-351 Request permission

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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