## Abstract

For a smooth fibre bundle\(F\mathop \to \limits^i E\mathop \to \limits^p B\) where*F* is a compact manifold with or without boundary, a vertical vector field*V* gives rise to a transfer τ_{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.

## Keywords

Vector Field Vector Bundle Compact Manifold Smooth Manifold Tubular Neighborhood
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## Bibliography

- [1]J.C. Becker andD. H. Gottlieb,
*The transfer map and fiber bundles*, Topology, 14 (1975), pp. 1–12zbMATHCrossRefMathSciNetGoogle Scholar - [2]J.C. Becker andD.H. Gottlieb,
*Transfer for fibrations and duality*, Compositio Mathematica,**33**(1976), pp. 107–133zbMATHMathSciNetGoogle Scholar - [3]D. H. Gottllieb,
*The trace of an action and the degree of a map*, Transactions A.M.S., 293 (1986), pp. 381–410CrossRefGoogle Scholar - [4]A. Dold,
*Fixed point index and fixed point theorem for Euclidean neighborhood retracts*, Topology, 4 (1965), pp. 1–8zbMATHCrossRefMathSciNetGoogle Scholar - [5]A. Dold,
*Transfer des points fixes d’une famille continue d’applications*, C.R. Acad. Sci. Paris Sér. A, 278 (1974), pp. 1291–1293zbMATHMathSciNetGoogle Scholar - [6]A. Dold,
*The fixed point index of fibre preserving maps*, Inventiones Math., 25 (1974), pp. 215–244CrossRefMathSciNetGoogle Scholar - [7]A. Dold,
*The fixed point transfer of fibre-preserving maps*, Math. Z., 148 (1976), pp. 215–244zbMATHCrossRefMathSciNetGoogle Scholar - [8]A. Dold,
*Fixed point theory and homotopy theory*, Contemporary Mathematics, 12 (1982), pp. 105–115zbMATHGoogle Scholar - [9]A. Dold and D. Puppe,
*Duality trace and transfer*, Proceedings of the Steklov Institute of Mathemataics, Issue 4 (1984), pp. 85–103Google Scholar - [10]Jan Rudzinski,
*Transfer and its reduction to coverings*, Bulletin de l’academie Polanaise des Sciences, serie des sciences mathematique, 27 (1979), pp. 913–921zbMATHMathSciNetGoogle Scholar

## Copyright information

© Springer-Verlag 1991