Equivariant cross sections of complex Stiefel manifolds


Onder T.

TOPOLOGY AND ITS APPLICATIONS, vol.109, no.1, pp.107-125, 2001 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 109 Issue: 1
  • Publication Date: 2001
  • Doi Number: 10.1016/s0166-8641(99)00149-2
  • Title of Journal : TOPOLOGY AND ITS APPLICATIONS
  • Page Numbers: pp.107-125

Abstract

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. (C) 2001 Elsevier Science B.V. All rights reserved.