ON THE CLASSIFICATION OF VECTOR BUNDLES WITH PERIODIC MAPS

Abdelouahab Arouche (1)

1 LATN-USTHB - Laboratoire d'algèbre et théorie des nombres

We give an explicit decription for univeral principal U(r)-bundles with periodic map by means of equivariant Stiefel manifolds. We then show that the associated equivariant vector bundle is equivalent to the canonical one given by G. Segal. Finally, we investigate some ideals involved in the equivariant K-theory of this classifying space.

Mots clés: Stiefel manifolds; equivariant bundles; completion

Domaines: Topologie algébrique [math.AT]; K-théorie et homologie [math.KT]

Abdelouahab Arouche. ON THE CLASSIFICATION OF VECTOR BUNDLES WITH PERIODIC MAPS. 2005. ⟨hal-00007974⟩