Results 281 to 290 of about 6,563,661 (318)
A Poincaré inequality on loop spaces
Journal of Functional Analysis, 2010 We investigate properties of measures in infinite dimensional spaces in terms of Poincaré inequalities. A Poincaré inequality states that the $L^2$ variance of an admissible function is controlled by the homogeneous $H^1$ norm. In the case of Loop spaces, it was observed by L.
Xin Chen, Xue-Mei Li
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The Suspension of a Loop Space
American Journal of Mathematics, 1958Let i: SX-* 93X be the identification map, where 3X is the reduced suspension. G. WV. Whitehead [17] studied the homotopy suspension E: rn (X) +, (SX) by using the map +(i): X -I?eaX. We consider a dual situation: abbreviate 0 (X, x0) by 2, and let j: Q? -> f2 be the identity.
Barcus, W. D., Meyer, J.-P.
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On the Free Loop Space of Homogeneous Spaces
American Journal of Mathematics, 1987This paper shows that if M is a compact simply connected homogeneous space which is not diffeomorhic to a symmetric space of rank one, then the Betti numbers with \({\mathbb{Z}}_ 2\)-coefficients of the free loop space of M are unbounded. As a corollary, the authors extend a result of Gromoll-Meyer to show that any Riemannian metric on M has infinitely
McCleary, John, Ziller, Wolfgang
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Journal of Knot Theory and Its Ramifications, 1999
We prove that the rack and quandle spaces of links in 3-manifolds, considered only as topological spaces (disregarding their cubical structure), are closely related to certain subspaces of the loop spaces on the 3-manifold, which we call the vertical and the straight loop space of the link. Using these models we prove that the homotopy type of the non-
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We prove that the rack and quandle spaces of links in 3-manifolds, considered only as topological spaces (disregarding their cubical structure), are closely related to certain subspaces of the loop spaces on the 3-manifold, which we call the vertical and the straight loop space of the link. Using these models we prove that the homotopy type of the non-
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Analysis on Loop Spaces and Topology
Mathematical Notes, 2002This is a survey paper on analysis on loop spaces and topology, important for topology and quantum field theory. The survey consists of the following sections, whose titles describe the content of the paper: Sobolev cohomology of loop spaces; Stochastic Chen-Souriau cohomologies; The De Rham-Hodge-Kodaira decomposition; Quotients of loop groups and ...
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Holomorphic Dynamics in Loop Spaces
Journal of Dynamical and Control Systems, 2006The authors describe a natural setting for studying a frequently encountered type of evolution of loops with respect to complex time. This evolution is studied on the language of holomorphic doughnuts with an emphasis on the existence problem and geometric aspects.
Aliashvili, T., Khimshiashvili, G.
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Loop expansion in a functional space
Physical Review D, 1989As an alternative to the loop expansion of the effective potential, wesuggest a functional expansion of the generating functional for an/ital n/-point Euclidean Green's function. The formulation of the scheme isindependent of the space-time dimension of the model.
, Kröger, , Labelle
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Loop Spaces and the hypoelliptic Laplacian
Communications on Pure and Applied Mathematics, 2007AbstractThe purpose of this paper is to introduce some ideas that motivated the construction of the hypoelliptic Laplacian as a deformation of Hodge theory, which interpolates between Hodge theory and the geodesic flow. Results obtained with Lebeau on the analysis of the hypoelliptic Laplacian are also presented. © 2007 Wiley Periodicals, Inc.
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Evolution of current loops in space
Astrophysics and Space Science, 1995Ampere’s law requires that every magnetic field have an associated current. The analysis of magnetic fields in this paper begins with that current in a circular loop and calculates the forces that make the loop evolve. A circular current generates a dipole field; and a second-order, ordinary differential equation represents the evolving magetic field ...
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Shape loop space of pro-discrete spaces
2022Loop spaces endowed with a (natural) compact-open topology are important invariants in (algebraic) topology. In the paper [Topology Appl. 261, 29--38 (2019; Zbl 1430.55008)], the author and \textit{B. Mashayekhy} introduced the \(k\)-th shape loop space \(\Omega_{k}^{p}(X,x)\) for the fixed polyhedral expansion \(p:(X,x)\to((X_\lambda,x_\lambda),[p_ ...
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