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We know that the sum of singularity index of the vector fields on a sphere equal to Euler characteristics of sphere, satisfying the Poincare-Hopf theorem. But how about situations of the geometry with edges and corners?

And if you can provide related references, I will be more appreciated.

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  • $\begingroup$ mathoverflow.net/q/415487/83537 $\endgroup$
    – Brevan Ellefsen
    Commented Feb 27, 2023 at 9:36
  • $\begingroup$ But I need some reference. Like journals or books. $\endgroup$
    – Hing Cu
    Commented Feb 27, 2023 at 11:06
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    $\begingroup$ The quoted question has a reference (inside the quotation): Guillemin and Pollack. Have you checked that source already? $\endgroup$
    – Sebastian Goette
    Commented Feb 27, 2023 at 14:35
  • $\begingroup$ Oh, yeah. Thanks very much for remindering. $\endgroup$
    – Hing Cu
    Commented Feb 28, 2023 at 8:52

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