Researchers demonstrate a systematic proof linking complex vector fields and manifold topology, suggesting elegant connections between concepts.
In this paper, we give a more elegant and systematic proof of Jacobowitz’s theorem which relates complex vector fields and the topology of the underlying manifold. The method we use is due to Atiyah [ Vector fields on manifolds (English, with French and German summaries), Westdeutscher Verlag, Cologne, 1970], who applied it to the study of real vector fields and characteristic numbers.
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Mengge Hu (2026) studied this question.
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