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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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by Sadayoshi Kojima and Yasushi Yamashita PDF
Proc. Amer. Math. Soc. 117 (1993), 845-851 Request permission

Abstract:

In this paper we construct a natural geometric structure for the space of shapes of a star-shaped polygon. Roughly speaking we find: The set of similarity classes of marked stars forms a hyperbolic right angle pentagon bundle over the space of external angle sets of inscribed pentagons. The assignment of the shape of its fiber to each angle set forms a hyperbolic plane bundle over the Teichmüller space of hyperbolic right angle pentagons. Any automorphism induced by renumbering is compatible with these geometric structures.
References
  • Makoto Sakuma, The geometries of spherical Montesinos links, Kobe J. Math. 7 (1990), no. 2, 167–190. MR 1096689
    • W. P. Thurston, Shapes of polyhedra, preprint, 1987.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 117 (1993), 845-851
  • MSC: Primary 57M50; Secondary 51M04, 51M09, 51M20
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1111430-3
  • MathSciNet review: 1111430