Equivariant cross sections of complex Stiefel manifolds
type: Item
instance of: scholarly article
title: Equivariant cross sections of complex Stiefel manifolds
zbMATH Open document ID: 0976.57032
DOI: 10.1016/S0166-8641(99)00149-2
author: Önder, Turgut
published in: Topology and its Applications
publication date: 2002-01-02T00:00:00Z
Mathematics Subject Classification ID: 57R91
Mathematics Subject Classification ID: 55R91
Mathematics Subject Classification ID: 55R50
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57R25
Mathematics Subject Classification ID: 55R25
Mathematics Subject Classification ID: 22A25
zbMATH DE Number: 1566037
zbMATH Keywords: complex Stiefel manifolds
zbMATH Keywords: equivariant fibre spaces
zbMATH Keywords: equivariant cross section
review text: Let \(G\) be a topological group, \(M\) be a unitary representation space of \(G\), and \(S(M)\) be the unit sphere of \(M\). Let \(W_k(M)\) be the Stiefel manifold of unitary \(k\)-frames on \(M\). The projection map \(W_k(M)\rightarrow S(M)\) sending a unitary \(k\)-frame \((u_1,\ldots,u_k)\) to \(u_k\) is \(G\)-equivariant. The author gives some necessary and sufficient conditions for the existence of a \(G\)-equivariant cross section of \(W_k(M)\) for certain finite group actions, under mild fixed point conditions. When \(G\) acts trivially, this is answered in [\textit{M. F. Atiyah} and \textit{J. A. Todd}, Proc. Camb. Philos. Soc. 56, 342-353 (1960; Zbl 0109.16102); \textit{J. F. Adams} and \textit{G. Walker}, ibid. 61, 81-103 (1965; Zbl 0142.40903)].
MaRDI profile type: Publication
cites work: On the groups \(J(X)\). I
cites work: Q5518126
cites work: Q3845883
cites work: The Span of Spherical Space Forms
cites work: Q3704110
cites work: Transformation groups and representation theory
cites work: The equivariant Dold theorem mod k and the Adams conjecture
cites work: The equivariant span of the unit spheres in representation spaces
cites work: On the equivariant J-groups. I
cites work: Equivariant Vector Fields on Spheres
cites work: Equivariant frame fields on spheres with complementary equivariant complex structures
cites work: Q3891421
cites work: Equivariant K-theory
cites work: Equivariant Fibrations and Transfer
reviewed by: Vladimir L. Popov
description: scientific article; zbMATH DE number 1566037