Global Classification of Generic Multi-vector Fields of Top Degree
نویسنده
چکیده
For any compact oriented manifold M , we show that that the top degree multi-vector fields transverse to the zero section of ∧TM are classified, up to orientation preserving diffeomorphism, in terms of the topology of the arrangement of its 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 spheres Sn, a correspondence between certain isotopy classes of multi-vector fields and classes of weighted signed trees is established.
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