View source for Solv manifold, compact

''compact solvmanifold''

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

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  L. Auslander,   "An exposition of the structure of solvmanifolds. Part I: Algebraic theory"  ''Bull. Amer. Math. Soc.'' , '''79''' :  2  (1973)  pp. 227–261</TD></TR></table>



====Comments====
Cf. also [[Solv manifold|Solv manifold]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  G.D. Mostow,   "Cohomology of topological groups and solvmanifolds"  ''Ann. of Math.'' , '''73'''  (1961)  pp. 20–48</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  R.W. Johnson,   "Presentations of solvmanifolds"  ''Ann. of Math.'' , '''94'''  (1972)  pp. 82–102</TD></TR></table>