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Look into the work of Søren Eilers

https://arxiv.org/abs/math/0504039

https://www.tandfonline.com/doi/abs/10.4169/amer.math.monthl...

(for the latter: use sci-hub)

Then there is also work for the 2D case by Tricia Muldoon Brown:

https://www.sciencedirect.com/science/article/pii/S0012365X1...

https://arxiv.org/abs/1608.01562

as well as by Alexander M. Haupt:

https://arxiv.org/abs/1810.10428




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