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A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.

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Can vector fields in manifolds with corner and sharp edges still satisfy Poincare-Hopf theorem?

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 …
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