Bordisme de S 1 -fibrés vectoriels munis¶de structures supplémentaires

Abstract

Bordism of S1-vector bundles with additional structures We give isomorphisms between equivariant bordism groups of certain S1-vector bundles and bordism groups of suitable “classifying” spaces determined by certain caracterestic classes. In the spinorial case, we detect the even or odd type of the S1-action and give a relationship with elleptic homology. Furthermore, we define a new type of $S^1$-actions, depending on the actions and the given slice type. This new type differs, in certain cases, from the classical odd or even type of S1-actions on spinorial manifolds.