Solv manifold, compact

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compact solvmanifold

A compact quotient space of a connected solvable Lie group (cf. Lie group, solvable; sometimes, however, compactness is not required). A particular case is a nil manifold. Compared with the latter the general case is considerably more complicated, but there is a complete structure theory for it too.


[1] L. Auslander, "An exposition of the structure of solvmanifolds. Part I: Algebraic theory" Bull. Amer. Math. Soc. , 79 : 2 (1973) pp. 227–261


Cf. also Solv manifold.


[a1] G.D. Mostow, "Cohomology of topological groups and solvmanifolds" Ann. of Math. , 73 (1961) pp. 20–48
[a2] R.W. Johnson, "Presentations of solvmanifolds" Ann. of Math. , 94 (1972) pp. 82–102
How to Cite This Entry:
Solv manifold, compact. Encyclopedia of Mathematics. URL:,_compact&oldid=36249
This article was adapted from an original article by D.V. Anosov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article