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Global Classification of Generic Multi‐Vector Fields of Top Degree
Author(s) -
Torres David Martínez
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703005143
Subject(s) - vector field , mathematics , diffeomorphism , degree (music) , isotopy , zero (linguistics) , vector bundle , topology (electrical circuits) , pure mathematics , infinitesimal , mathematical analysis , manifold (fluid mechanics) , geometry , combinatorics , physics , linguistics , philosophy , acoustics , mechanical engineering , engineering
For any closed oriented manifold M , the top degree multi‐vector fields transverse to the zero section of ∧ 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.