Vector fields and transfers

Abstract

For a smooth fibre bundle\(F\mathop \to \limits^i E\mathop \to \limits^p B\) whereF is a compact manifold with or without boundary, a vertical vector fieldV gives rise to a transfer τV as anS-map. Our goal is to show these transfers satisfy an equation analogous to one that the index of vector fields satisfy. This equation gives results involving equivariant vector fields as well as a characterization of those transfers defined by vector fields in terms of the ordinary Euler-Poincare transfers.