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Global classification of generic multi-vector fields of top degree

David Martinez Torres
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Abstract

For any compact oriented manifold $M$, we show that that the top degree multi-vector fields transverse to the zero section of $\wedge^{\text{top}}TM$ 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 $S^n$, a correspondence between certain isotopy classes of multi-vector fields and classes of weighted signed trees is established.

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David Martinez Torres. 2018-07-30. Global classification of generic multi-vector fields of top degree. https://arxiv.org/abs/math/0209374

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