منابع مشابه
Homology of Planar Polygon Spaces
In this paper we study topology of the variety of closed planar n-gons with given side lengths l1, . . . , ln. The moduli space M` where ` = (l1, . . . , ln), encodes the shapes of all such n-gons. We describe the Betti numbers of the moduli spaces M` as functions of the length vector ` = (l1, . . . , ln). We also find sharp upper bounds on the sum of Betti numbers of M` depending only on the n...
متن کاملHomology of Planar Polygon
In this paper we study topology of the variety of closed pla-nar n-gons with given side lengths l1,. .. , ln. The moduli space M ℓ where ℓ = (l1,. .. , ln), encodes the shapes of all such n-gons. We describe the Betti numbers of the moduli spaces M ℓ as functions of the length vector ℓ = (l1,. .. , ln). We also find sharp upper bounds on the sum of Betti numbers of M ℓ depending only on the num...
متن کاملTopological Complexity of Planar Polygon Spaces with Small Genetic Code
We determine, within 1, the topological complexity of many planar polygon spaces mod isometry. In all cases considered except for those homeomorphic to real projective space or n-tori, the upper and lower bounds given by dimension and cohomology considerations differ by 1. The spaces which we consider are those whose genetic codes, in the sense of Hausmann and Rodriguez, have a single gene, and...
متن کاملPolygon Spaces and Grassmannians
We study the moduli spaces of polygons in R and R, identifying them with subquotients of 2-Grassmannians using a symplectic version of the Gelfand-MacPherson correspondence. We show that the bending flows defined by Kapovich-Millson arise as a reduction of the Gelfand-Cetlin system on the Grassmannian, and with these determine the pentagon and hexagon spaces up to equivariant symplectomorphism....
متن کاملExact Solution of Two Planar Polygon Models
Using a simple transfer matrix approach we have derived long series expansions for the perimeter generating functions of both three-choice polygons and punctured staircase polygons. In both cases we find that all the known terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 8. We report on an analysis of the properties of the differential equ...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2007
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-007-9139-7