Napoleon in isolation

Danny Calegari

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Napoleon in isolation

Danny Calegari

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Abstract

Napoleon's theorem in elementary geometry describes how certain linear operations on plane polygons of arbitrary shape always produce regular polygons. More generally, certain triangulations of a polygon that tiles R^2 admit deformations which keep fixed the symmetry group of the tiling. This gives rise to isolation phenomena in cusped hyperbolic 3-manifolds, where hyperbolic Dehn surgeries on some collection of cusps leaves the geometric structure at some other collection of cusps unchanged.

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Danny Calegari. 2000-02-23. Napoleon in isolation. https://arxiv.org/abs/math/9909106

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