Napoleon in isolation
Abstract
Description
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.
10 pages, 5 figures; minor changes. Accepted for publication in PAMS
10 pages, 5 figures; minor changes. Accepted for publication in PAMS