Bordism of \(S^1\)-vector bundles with additional structures (Q5945013)

This paper considers bordism groups of vector bundles with \(S^1\)-action having a given slice type, with the total space of the bundle having additional structure such as an orientation or spin structure. These are shown to be isomorphic to the bordism groups of certain classifying spaces. This type of bordism group arises when one tries to study circle actions on spin manifolds by working through the fixed point sets of subgroups.