# Solv manifold, compact

From Encyclopedia of Mathematics

*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.

#### References

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

#### Comments

Cf. also Solv manifold.

#### References

[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: http://www.encyclopediaofmath.org/index.php?title=Solv_manifold,_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