Napoleon in isolation
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- by Danny Calegari PDF
- Proc. Amer. Math. Soc. 129 (2001), 3109-3119 Request permission
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 $\mathbb {R}^2$ 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 leave the geometric structure at some other collection of cusps unchanged.References
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Additional Information
- Danny Calegari
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- Address at time of publication: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
- MR Author ID: 605373
- Email: dannyc@math.berkeley.edu, dannyc@math.harvard.edu
- Received by editor(s): June 15, 1999
- Received by editor(s) in revised form: March 6, 2000
- Published electronically: April 2, 2001
- Communicated by: Ronald A. Fintushel
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3109-3119
- MSC (2000): Primary 57M50, 57M25
- DOI: https://doi.org/10.1090/S0002-9939-01-05915-9
- MathSciNet review: 1840118