Vol. 15, No. 2, 1965

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 304: 1
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Euclidean fiberings of solvmanifolds

John Stuelpnagel

Vol. 15 (1965), No. 2, 705–717
Abstract

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
Milestones
Received: 14 April 1964
Published: 1 June 1965
Authors
John Stuelpnagel