Equivariant cross sections of complex Stiefel manifolds

✍ Scribed by Turgut Önder

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 179 KB
• Volume: 109
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00149-2

✦ Synopsis

Let G be a finite group and let M be a unitary representation space of G. A solution to the existence problem of G-equivariant cross sections of the complex Stiefel manifold W k (M) of unitary k-frames over the unit sphere S(M) is given under mild restrictions on G and on fixed point sets. In the case G is an even ordered group, some sufficient conditions for the existence of G-equivariant real frame fields on spheres with complementary G-equivariant complex structures are also obtained, improving earlier results about odd ordered groups.