Involve: A Journal of Mathematics
- Volume 2, Number 5 (2009), 495-509.
On the orbits of an orthogonal group action
Let be the Lie group and let be the vector space of real matrices. An action of on is given by
We consider the orbits of this group action and demonstrate a cross-section to the orbits. We then determine the stabilizer for a typical element in this cross-section and completely describe the fundamental group of an orbit of maximal dimension.
Involve, Volume 2, Number 5 (2009), 495-509.
Received: 8 April 2008
Accepted: 28 September 2009
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 22C05: Compact groups 57S15: Compact Lie groups of differentiable transformations
Secondary: 55Q52: Homotopy groups of special spaces
Czarnecki, Kyle; Howe, R. Michael; McTavish, Aaron. On the orbits of an orthogonal group action. Involve 2 (2009), no. 5, 495--509. doi:10.2140/involve.2009.2.495. https://projecteuclid.org/euclid.involve/1513799207