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### Constructing a vector field with given zeros on a torus

By the Hopf-PoincarĂ© theorem, the sum of the indices of the zeros of a vector field on the d-dimensional torus must equal zero. Given an even number of points $x_i$ on a d-dimensional torus, and ...

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### Special coordinates for periodic metrics

This question is a follow-up to that one.
Given a $\mathbb{Z}^n$-periodic metric $g$ on $\mathbb{R}^n$ (with $n>2$), is it possible to find a periodic diffeomorphism $\varphi$ such that ...