The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
The symplectic geometry of polygons in Euclidean space
Open accessAbstract
We study the symplectic geometry of moduli spaces M r of polygons with fixed side lengths in Euclidean space.We show that M r has a natural structure of a complex analytic space and is complex-analytically isomorphic to the weighted quotient of (5 2 ) n by PLS(2,C) constructed by Deligne and Mostow.We study the Hamiltonian flows on M r obtained by bending the polygon along diagonals and show the group generated by such flows acts transitively on M r .We also relate these flows to the twist flows of Goldman and Jeffrey-Weitsman.
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Cites
Invariant functions on Lie groups and Hamiltonian flows of surface group representations
Goldman, W. M. (1986) · Inventiones Mathematicae · doi:10.1007/bf01389091 · Cited by 441
Monodromy of hypergeometric functions and non-lattice integral monodromy
Deligne, P., & Mostow, G. D. (1986) · Publications mathématiques de l IHÉS · doi:10.1007/bf02831622 · Cited by 409
The deformation theory of representations of fundamental groups of compact Kähler manifolds
Goldman, W. M., & Millson, J. J. (1988) · Publications mathématiques de l IHÉS · doi:10.1007/bf02699127 · Cited by 353
Self-citationA Stratification of the Null Cone Via the Moment Map
Ness, L. A., & Mumford, D. B. (1984) · American Journal of Mathematics · doi:10.2307/2374395 · Cited by 220
Spatial Polygons and Stable Configurations of Points in the Projective Line
Klyachko, A. A. (1994) · Aspects of mathematics. E · doi:10.1007/978-3-322-99342-7_8 · Cited by 88
On the geometry of the planar 4-bar mechanism
Gibson, C. G., & Newstead, P. E. (1986) · Acta Applicandae Mathematicae · doi:10.1007/bf00051348 · Cited by 61
Cited by
Twisted geometries: A geometric parametrization of SU(2) phase space
Freidel, L., & Speziale, S. (2010) · Physical Review D · doi:10.1103/physrevd.82.084040 · Cited by 259
The Quantum Tetrahedron in 3 and 4 Dimensions
Baez, J. C., & Barrett, J. W. (1999) · arXiv · doi:10.48550/arxiv.gr-qc/9903060 · Cited by 146
The quantum tetrahedron in 3 and 4 dimensions
Baez, J. C., & Barrett, J. W. (1999) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1999.v3.n4.a3 · Cited by 146
Ding, Y., Han, M., & Rovelli, C. (2011) · Physical Review D · doi:10.1103/physrevd.83.124020 · Cited by 60
Metadata
- Authors
- Kapovich, M., & Millson, J. J.
- Venue
- Journal of Differential Geometry
- Publisher
- International Press of Boston
- Published
- 1996-01-01
- Volume
- 44
- Issue
- 3
- Pages
- 479-513
- ISSN
- 0022-040X (ISSN-L)
- OpenAlex
- W1571839244
- Cited by
- 259
- References
- 6
- FWCI
- 7.03
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Kapovich, M., & Millson, J. J. (1996). The symplectic geometry of polygons in Euclidean space. Journal of Differential Geometry. https://doi.org/10.4310/jdg/1214459218
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