Napoleon in isolation

Author:
Danny Calegari

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

Published electronically:
April 2, 2001

MathSciNet review:
1840118

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Abstract | References | Similar Articles | Additional Information

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 admit deformations which keep fixed the symmetry group of the tiling. This gives rise to *isolation phenomena* in cusped hyperbolic -manifolds, where hyperbolic Dehn surgeries on some collection of cusps leave the geometric structure at some other collection of cusps unchanged.

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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

Email:
dannyc@math.berkeley.edu, dannyc@math.harvard.edu

DOI:
https://doi.org/10.1090/S0002-9939-01-05915-9

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

Article copyright:
© Copyright 2001
American Mathematical Society