Vol. 15, No. 2, 1965

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Euclidean fiberings of solvmanifolds

John Stuelpnagel

Vol. 15 (1965), No. 2, 705–717

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.

Mathematical Subject Classification
Primary: 22.70
Secondary: 53.66
Received: 14 April 1964
Published: 1 June 1965
John Stuelpnagel