Solv manifold, compact
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.
|||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|
Solv manifold, compact. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Solv_manifold,_compact&oldid=36249