The symplectic geometry of polygons in Euclidean space
نویسندگان
چکیده
منابع مشابه
The Symplectic Geometry of Polygons in Hyperbolic 3-space∗
We study the symplectic geometry of the moduli spaces Mr = Mr(H) of closed n-gons with fixed side-lengths in hyperbolic three-space. We prove that these moduli spaces have almost canonical symplectic structures. They are the symplectic quotients of Bn by the dressing action of SU(2) (here B is the subgroup of the Borel subgroup of SL2(C) defined below). We show that the hyperbolic Gauss map set...
متن کاملThe toric geometry of triangulated polygons in Euclidean space
Speyer and Sturmfels [SpSt] associated Gröbner toric degenerations Gr2(C) of Gr2(Cn) to each trivalent tree T with n leaves. These degenerations induce toric degenerations M r of Mr, the space of n ordered, weighted (by r) points on the projective line. Our goal in this paper is to give a geometric (Euclidean polygon) description of the toric fibers as stratified symplectic spaces and describe ...
متن کاملThe Symplectic Geometry of Polygons inEuclidean
We study the symplectic geometry of moduli spaces M r of polygons with xed 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 (S 2) n constructed by Deligne and Mostow. We study the Hamiltonian ows on M r obtained by bending the polygon along diagonals and show the group generat...
متن کاملOn the Symplectic Volume of the Moduli Space of Spherical and Euclidean Polygons
In this paper, we study the symplectic volume of the moduli space of polygons by using Witten’s formula. We propose to use this volume as a measure for the flexibility of a polygon with fixed side-lengths. The main result of our is that among all the polygons with fixed perimeter in S or E the regular one is the most flexible and that among all the spherical polygons the regular one with side-l...
متن کاملThe Symplectic Geometry of Polygons in the 3-sphere
Abstract. We study the symplectic geometry of the moduli spaces Mr = Mr(S ) of closed n-gons with fixed side-lengths in the 3-sphere. We prove that these moduli spaces have symplectic structures obtained by reduction of the fusion product of n conjugacy classes in SU(2), denoted C r , by the diagonal conjugation action of SU(2). Here C n r is a quasi-Hamiltonian SU(2)-space. An integrable Hamil...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1996
ISSN: 0022-040X
DOI: 10.4310/jdg/1214459218