International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 8, Pages 453-469

An introduction to spherical orbit spaces

Jill Mcgowan1 and Catherine Searle2

1Department of Mathematics, Howard University, Washington 20059, DC, USA
2Instituto de Mathemáticas de la UNAM, Unidad Cuernavaca, Avenida Universidad S/N, Colonia lo Mas de Chamilpa, Cuernavaca 62210, Morelos, Mexico

Received 21 February 2001; Revised 24 September 2001

Copyright © 2002 Jill Mcgowan and Catherine Searle. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Consider a compact, connected Lie group G acting isometrically on a sphere Sn of radius 1. Two-dimensional quotient spaces of the type Sn/G have been investigated extensively. This paper provides an elementary introduction, for nonspecialists, to this important field by way of several classical examples and supplies an explicit list of all the isotropy subgroups involved in these examples.