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Vector fields and transfers

manuscripta mathematica volume 72, pages 111–130 (1991)Cite this article

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.

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Bibliography

  1. J.C. Becker andD. H. Gottlieb,The transfer map and fiber bundles, Topology, 14 (1975), pp. 1–12

    Article  MATH  MathSciNet  Google Scholar 

  2. J.C. Becker andD.H. Gottlieb,Transfer for fibrations and duality, Compositio Mathematica,33 (1976), pp. 107–133

    MATH  MathSciNet  Google Scholar 

  3. D. H. Gottllieb,The trace of an action and the degree of a map, Transactions A.M.S., 293 (1986), pp. 381–410

    Article  Google Scholar 

  4. A. Dold,Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology, 4 (1965), pp. 1–8

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Dold,Transfer des points fixes d’une famille continue d’applications, C.R. Acad. Sci. Paris Sér. A, 278 (1974), pp. 1291–1293

    MATH  MathSciNet  Google Scholar 

  6. A. Dold,The fixed point index of fibre preserving maps, Inventiones Math., 25 (1974), pp. 215–244

    Article  MathSciNet  Google Scholar 

  7. A. Dold,The fixed point transfer of fibre-preserving maps, Math. Z., 148 (1976), pp. 215–244

    Article  MATH  MathSciNet  Google Scholar 

  8. A. Dold,Fixed point theory and homotopy theory, Contemporary Mathematics, 12 (1982), pp. 105–115

    MATH  Google Scholar 

  9. A. Dold and D. Puppe,Duality trace and transfer, Proceedings of the Steklov Institute of Mathemataics, Issue 4 (1984), pp. 85–103

  10. Jan Rudzinski,Transfer and its reduction to coverings, Bulletin de l’academie Polanaise des Sciences, serie des sciences mathematique, 27 (1979), pp. 913–921

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA

    James C. Becker & Daniel Henry Gottlieb

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  1. James C. Becker
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  2. Daniel Henry Gottlieb
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Becker, J.C., Gottlieb, D.H. Vector fields and transfers. Manuscripta Math 72, 111–130 (1991). https://doi.org/10.1007/BF02568269

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  • DOI: https://doi.org/10.1007/BF02568269

Keywords

  • Vector Field
  • Vector Bundle
  • Compact Manifold
  • Smooth Manifold
  • Tubular Neighborhood