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Search Results: 1 - 10 of 23178 matches for " Jean-Claude Hausmann "
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Contr?le des bras articulés et transformations de Moebius (Control of robot arms and Moebius transformations)
Jean-Claude Hausmann
Mathematics , 2002,
Abstract: For a m-tuple a=(a_1,...,a_m) of positive real numbers, the robot arm of type a in R^d is the map f^a:(S^{d-1})^m -> R^d defined by f^a(z_1,...,z_m) to be the sum of the a_jz_j's. Our aim is to attack the inverse problem via the horizontal liftings for the distribution Delta^a orthogonal to the fibers of f^a. One shows that the connected components by horizontal curves are the orbits of an actiion on (S^{d-1})^m by a product of groups of Moebius transformations. In several cases, the holonomy orbits of the distribution Delta^a are also described.
Geometric descriptions of polygon and chain spaces
Jean-Claude Hausmann
Mathematics , 2007,
Abstract: We give a few simple methods to geometically describe some polygon and chain-spaces in R^d. They are strong enough to give tables of m-gons and m-chains when m <= 6.
Counting polygon spaces, Boolean functions and majority games
Jean-Claude Hausmann
Mathematics , 2015,
Abstract: We explain why numbers occurring in the classification of polygon spaces coincide with numbers of self-dual equivalence classes of threshold functions, or of regular Boolean functions, or of decisive weighted majority games.
Triangles on planar Jordan $C^1$-curves
Jean-Claude Hausmann
Mathematics , 2012,
Abstract: We prove that a Jordan $\calc^1$-curve in the plane contains any non-flat triangle up to translation and homothety with positive ratio. This is false if the curve is not $C^1$. The proof uses a bit configuration spaces, differential and algebraic topology as well as the Schoenflies theorem. A partial generalization holds true in higher dimensions.
Théorie de jauge et groupo\"?des (Gauge theory and groupoids)
Jean-Claude Hausmann
Mathematics , 1999,
Abstract: We consider the problem of existence of representations of topological groupoids on a principal bundle and the classification of such representations up to gauge transformation. Such representations naturally occur in various contexts such as gauge theory, lattice gauge fields, equivariant bundles, etc. In the course of the proofs, some new facts about Milnor's classifying spaces and gauge groups are established.
Holonomy orbits of the snake charmer algorithm
Jean-Claude Hausmann,Eugenio Rodriguez
Mathematics , 2006,
Abstract: The snake charmer algorithm permits us to deform a piecewise smooth curve starting from the origin in R^d, so that its end follows a given path. When this path is a loop, a holonomy phenomenon occurs. We prove that the holonomy orbits are closed manifolds diffeomorphic to real Stiefel manifolds. A survey of the snake charmer algorithm is given in the paper.
Conjugation spaces and 4-manifolds
Ian Hambleton,Jean-Claude Hausmann
Mathematics , 2009,
Abstract: We show that 4-dimensional conjugation manifolds are all obtained from branched 2-fold coverings of knotted surfaces in Z/2-homology 4-spheres.
Simple Hamiltonian manifolds
Jean-Claude Hausmann,Tara S. Holm
Mathematics , 2010,
Abstract: A simple Hamiltonian manifold is a closed connected symplectic manifold equipped with a Hamiltonian action of a torus T with moment map Phi: M-->t^*, such that the fixed set M^T has exactly two connected components, denoted M_0 and M_1. We study the differential and symplectic geometry of simple Hamiltonian manifolds, including a large number of examples.
The cohomology ring of polygon spaces
Jean-Claude Hausmann,Allen Knutson
Mathematics , 1997,
Abstract: We compute the integer cohomology rings of the ``polygon spaces'' introduced in [Hausmann,Klyachko,Kapovich-Millson]. This is done by embedding them in certain toric varieties; the restriction map on cohomology is surjective and we calculate its kernel using ideas from the theory of Gr\"obner bases. Since we do not invert the prime 2, we can tensor with Z/2; halving all degrees we show this produces the Z/2 cohomology rings of planar polygon spaces. In the equilateral case, where there is an action of the symmetric group permuting the edges, we show that the induced action on the integer cohomology is _not_ the standard one, despite it being so on the rational cohomology [Kl]. Finally, our formulae for the Poincar\'e polynomials are more computationally effective than those known [Kl].
Polygon spaces and Grassmannians
Jean-Claude Hausmann,Allen Knutson
Mathematics , 1996,
Abstract: We study the moduli spaces of polygons in R^2 and R^3, identifying them with subquotients of 2-Grassmannians using a symplectic version of the Gel'fand-MacPherson correspondence. We show that the bending flows defined by Kapovich-Millson arise as a reduction of the Gel'fand-Cetlin system on the Grassmannian, and with these determine the pentagon and hexagon spaces up to equivariant symplectomorphism. Other than invocation of Delzant's theorem, our proofs are purely polygon-theoretic in nature.
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