A generalized Poincar\'e-Hopf index theorem

Beno\^it Jubin

A generalized Poincar\'e-Hopf index theorem

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arxiv 0903.0697 v2 pith:2SJCRLZM submitted 2009-03-04 math.DG

Benoît Jubin This is my paper · ORCID

classification math.DG

keywords e-hopfindexpoincartheoremapplyboundarycomplexfields

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We state and prove a generalization of the Poincar\'e-Hopf index theorem for manifolds with boundary. We then apply this result to non-vanishing complex vector fields.

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Regularity Conditions for Critical Point Convergence
math.GN 2025-07 conditional novelty 7.0 of 10

With C1 convergence plus a positive lower bound on critical point spacing, maxima, minima, and saddle counts converge; with C2 convergence to a Morse function, Morse index counts converge.

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