Spaces of polygons in the plane and morse theory

American Mathematical Monthly

Volumn 112, Issue 4, 2005, Pages 289-310

  Shimamoto, Don ^a   Vanderwaart, Catherine ^a  

^a SWARTHMORE COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17544381856     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.2307/30037466     Document Type: Article

References (21)

1. M. Artin, Algebra, Prentice-Hall, Upper Saddle River, NJ, 1991.
2. L. Asimow and B. Roth, The rigidity of graphs, Trans. Amer. Math. Soc. 245 (1978) 279-289.
3. A. Browder, Mathematical Analysis: An Introduction, Springer-Verlag, New York, 1996.
4. R. Connelly and E. D. Demaine, Geometry and topology of polygonal linkages, in Handbook of Discrete and Computational Geometry, 2nd ed., J. E. Goodman and J. O'Rourke, eds., Chapman & Hall/CRC, Boca Raton, FL, 2004, pp. 197-218.
5. R. Connelly, E. Demaine, and G. Rote, Straightening polygonal arcs and convexifying polygonal cycles, Discrete Comput. Geom. 30 (2003) 205-239.
6. F. R. Gantmacher, The Theory of Matrices, vol. 1, Chelsea, New York, 1960.
7. J.-C. Hausmann, Sur la topologie des bras articules, in Algebraic Topology, Poznán, 1989, Lecture Notes in Mathematics, no. 1474, Springer-Verlag, Berlin, 1991, pp. 146-159.
8. J.-C. Hausmann and A. Knutson, The cohomology ring of polygon spaces, Ann. Inst. Fourier (Grenoble) 48 (1998) 281-321.
9. T. F. Havel, Some examples of the use of distances as coordinates for Euclidean geometry, J. Symbolic Comput. 11 (1991) 579-593.
10. D. Jordan and M. Steiner, Compact surfaces as configuration spaces of mechanical linkages, Israel J. Math. 122 (2001) 175-187.
11. M. Kapovich and J. Millson, On the moduli space of polygons in the Euclidean plane, J. Differential Geom. 42 (1995) 430-464.
12. _, The symplectic geometry of polygons in Euclidean space, J. Differential Geom. 44 (1996) 479-513.
13. _, Universality theorems for configuration spaces of planar linkages, Topology 41 (2002) 1051-1107.
14. H. C. King, Planar linkages and algebraic sets, in Proceedings of 6th Gökova Geometry-Topology Conference, Turkish J. Math. 23 (1999) 33-56.
15. P. A. Kirk and E. P. Klassen, Representation spaces of Seifert fibered homology spheres. Topology 30 (1991) 77-95.
16. W. J. Lenhart and S. H. Whitesides, Reconfiguring closed polygonal chains in Euclidean d-space. Discrete Comput. Geom. 13(1995) 123-140.
17. R. J. Milgram and J. C. Trinkle, The geometry of configuration spaces for closed chains in two and three dimensions, Homology Homotopy Appl. 6 (2004) 237-267.
18. J. Milnor, Morse Theory, Princeton University Press, Princeton, 1969.
19. J. R. Munkres, Analysis on Manifolds, Westview, Boulder, CO, 1991.
20. W. P. Thurston and J. R. Weeks, The mathematics of three-dimensional manifolds, Scientific American 251 (July, 1984) 108-120.
21. K. Walker, Configuration Spaces of Linkages, undergraduate thesis, Princeton University, 1985.