Vector fields and transfers | Zendy

James C. Becker | Zendy; Daniel Henry Gottlieb | Zendy

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Vector fields and transfers

Author(s) -

James C. Becker,

Daniel Henry Gottlieb

Publication year - 1991

Publication title -

manuscripta mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.752

H-Index - 46

eISSN - 1432-1785

pISSN - 0025-2611

DOI - 10.1007/bf02568269

Subject(s) - mathematics , vector field , vector bundle , equivariant map , boundary (topology) , solenoidal vector field , vector valued differential form , manifold (fluid mechanics) , field (mathematics) , pure mathematics , number theory , mathematical analysis , fundamental vector field , frame bundle , algebra over a field , normal bundle , geometry , mechanical engineering , engineering , lie conformal algebra , adjoint representation of a lie algebra

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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