Solv manifold, compact

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