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GLOBAL CLASSIFICATION OF GENERIC MULTI-VECTOR FIELDS OF TOP DEGREE

Published online by Cambridge University Press:  24 May 2004

DAVID MARTÍNEZ TORRES
Affiliation:
Departamento de Matematicas, Universidad Carlos III, Avenida Universidad 30, 28911 Leganés, Madrid, [email protected]
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Abstract

For any closed oriented manifold $M$, the top degree multi-vector fields transverse to the zero section of $\wedge^{{\rm top}}TM$ are classified, up to orientation preserving diffeomorphism, in terms of the topology of the arrangement of their zero locus and a finite number of numerical invariants. The group governing the infinitesimal deformations of such multi-vector fields is computed, and an explicit set of generators exhibited. For the sphere $S^n$, a correspondence between certain isotopy classes of multi-vector fields and classes of weighted signed trees is established.

Type
Notes and Papers
Copyright
The London Mathematical Society 2004

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Footnotes

The author was supported by an FPU grant of the Spanish Ministry of Education and a grant of the Fundación Universidad Carlos III de Madrid.