VECTOR-FIELDS AND TRANSFERS

For a smooth fibre bundle [GRAPHICS] where F is a compact manifold with or without boundary, a vertical vector field V gives rise to a transfer tau-V as an S-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.