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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The classification of flat solvmanifolds
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by Alexander Morgan PDF
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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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 239 (1978), 321-351
  • MSC: Primary 22E25
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0470138-4
  • MathSciNet review: 0470138