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Homology of the configuration spaces of quasi-equilateral polygon linkages


Authors: Yasuhiko Kamiyama, Michishige Tezuka and Tsuguyoshi Toma
Journal: Trans. Amer. Math. Soc. 350 (1998), 4869-4896
MSC (1991): Primary 55R55; Secondary 51N20
DOI: https://doi.org/10.1090/S0002-9947-98-02348-4
MathSciNet review: 1615983
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Abstract: We consider the configuration space $M_{n,r}$ of quasi-equilateral polygon linkages with $n$ vertices each edge having length $1$ except for one fixed edge having length $r \; (r \geq 0)$ in the Euclidean plane $\mathbf{R}^{2}.$ In this paper, we determine $H_{\ast }(M_{n,r}; \mathrm{\bf Z})$.


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  • [1] A. Bousfield and D. Kan, Homotopy limits, completions and localizations, Lecture Notes in Math., vol. 304, Springer-Verlag, 1972. MR 51:1825
  • [2] J.-C. Hausmann, Sur la topologie des bras articulés, Algebraic Topology, Pozna\'{n} 1989, Lecture Notes in Math., vol. 1474, Springer-Verlag, 1991, pp. 146-159. MR 93a:57035
  • [3] T. Havel, Some examples of the use of distances as coordinates in Euclidean geometry, Journal of Symbolic Computation 11 (1991), 579-593. MR 92j:51033
  • [4] Y. Kamiyama, An elementary proof of a theorem of T. F. Havel, Ryukyu Math. J. 5 (1992), 7-12. MR 94a:52044
  • [5] Y. Kamiyama, Topology of equilateral polygon linkages, Top. and its Applications 68 (1996), 13-31. MR 96j:52041
  • [6] M. Kapovich and J. Millson, On the moduli space of polygons in the Euclidean plane, Journal of Diff. Geometry 42 (1995), 133-164. MR 98b:52019
  • [7] M. Kato, Topology of $k$-regular spaces and algebraic sets, Manifolds-Tokyo 1973, Univ. of Tokyo Press, Tokyo, 1975, pp. 153-159. MR 54:6149
  • [8] J. Milnor, Morse theory, Ann. of Math. Studies, vol. 51, Princeton Univ. Press, Princeton, 1963. MR 29:634
  • [9] J. Milnor, Singular points of complex hypersurfaces, Ann. of Math. Studies, vol. 61, Princeton Univ. Press, Princeton, 1968. MR 39:969
  • [10] I. Schoenberg, Linkages and distance geometry. I. Linkages, Indag. Math. 31 (1969), 42-52. MR 39:7512
  • [11] T. Toma, An analogue of a theorem of T. F. Havel, Ryukyu Math. J. 6 (1993), 69-77; Corrections, ibid. 8 (1995), 95-96. MR 95g:52038

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Additional Information

Yasuhiko Kamiyama
Affiliation: Department of Mathematics, University of the Ryukyus, Nishihara-Cho, Okinawa 903-01, Japan
Email: kamiyama@sci.u-ryukyu.ac.jp

Michishige Tezuka
Affiliation: Department of Mathematics, University of the Ryukyus, Nishihara-Cho, Okinawa 903-01, Japan
Email: tez@sci.u-ryukyu.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-98-02348-4
Keywords: Polygon, linkage, homology
Received by editor(s): December 21, 1995
Article copyright: © Copyright 1998 American Mathematical Society

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