Homotopy groups of some homogeneous spaces and some remarks on their sections over the sphere

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Önder M. T., Abdelal M.

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, vol.139, no.3, pp.381-394, 1990 (Scopus)

• Publication Type: Article / Article
• Volume: 139 Issue: 3
• Publication Date: 1990
• Journal Name: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO
• Journal Indexes: Scopus
• Page Numbers: pp.381-394
• Middle East Technical University Affiliated: Yes

Abstract

Stable homotopy groups and a few of the unstable homotopy groups

of the homogeneous spaces SO(2n)/U(s) and U(2n)/Sp(s) for s < n,

and those of SO(4n)/Sp(s) for s <_ n are computed. The enumeration

of homotopy classes of normalized almost complex (n--1) and (n- 2)

substructures with oriented framed complements are given. Some results about

the existence of the equivariant cross sections of these homogeneous spaces

over the spheres with respect to certain unitary group actions are proved