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Compact solvmanifolds of dimension at most 4

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Abstract

We study compact solvmanifolds of dimension 3 and 4 (the cases of dimension 1 and 2 are almost trivial). We give a detailed description of these solvmanifolds up to diffeomorphism in terms of the fundamental group and its decomposition into a semidirect product. We study the peculiarities of the topological structure of the solvmanifolds of this type; in particular, those connected with the Mostow fibration and the decomposability of solvmanifolds into a direct product of manifolds of less dimension. We distinguish special classes of these solvmanifolds and the corresponding classes of fundamental groups.

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Author information

Correspondence to V. V. Gorbatsevich.

Additional information

Original Russian Text Copyright © 2009 Gorbatsevich V. V.

The author was supported by the Russian Foundation for Basic Research (Grant 07-01-00230).

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Moscow. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 2, pp. 300–319, March–April, 2009.

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Gorbatsevich, V.V. Compact solvmanifolds of dimension at most 4. Sib Math J 50, 239–252 (2009). https://doi.org/10.1007/s11202-009-0028-1

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Keywords

  • solvmanifold
  • Mostow fibration