|
This paper is concerned with
the problem of finding conditions on a solvable Lie group G and a closed
subgroup H which are sufficient for G∕H to have topological structure of a fiber
bundle with compact base space and euclidean fiber (if this is the case, we say
that G∕H has a euclidean fibering). The main results are the following two
theorems.
Theorem 5.3. Let G be a connected solvable linear Lie group, and H a closed
subgroup which splits in G. Then G∕H has a euclidean fibering.
Theorem 5.4. Let G be a connected solvable matrix group, and assume that G is
of finite index in its algebraic group hull. Then for any closed subgroup H of G, G∕H
has a euclidean fibering.
To the best of the autlior’s knowledge, these are the first results on existence of
such fiberings which do not require that the isotropy subgroup H have a finite
number of connected components.
|
