GLOBAL CLASSIFICATION OF GENERIC MULTI-VECTOR FIELDS OF TOP DEGREE
Published online by Cambridge University Press: 24 May 2004
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.
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- The London Mathematical Society 2004
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