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Napoleon in isolation
Author(s):
Danny
Calegari
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3109-3119.
MSC (2000):
Primary 57M50, 57M25
Posted:
April 2, 2001
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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  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:
10.1090/S0002-9939-01-05915-9
PII:
S 0002-9939(01)05915-9
Received by editor(s):
June 15, 1999
Received by editor(s) in revised form:
March 6, 2000
Posted:
April 2, 2001
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2001,
American Mathematical Society
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