منابع مشابه
K-theory of Morse geodesics
We develop the K-theory of a C∗–algebra Oλ which represents the leaf space of measured foliations studied by Novikov, Masur, Thurston and Veech. The K-theory construction is based on the coding of geodesic lines due to Koebe and Morse. This method allows to calculate the range of Elliott group (K0, K + 0 , [1]) of Oλ, to establish a condition of strict ergodicity of the interval exchange transf...
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We show that the index of a lightlike geodesic in a conformally standard stationary spacetime (M0 × R, g) is equal to the index of its spatial projection as a geodesic of a Finsler metric F on M0 associated to (M0×R, g). Moreover we obtain the Morse relations of lightlike geodesics connecting a point p to a curve γ(s) = (q0, s) by using Morse theory on the Finsler manifold (M0, F ). To this end...
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Let f ∈ C(M,R) be a functional defined on a Hilbert manifold M. It is well known that if f is a Morse functional (i.e. every critical point of f is nondegenerate) and f satisfies the so called Palais–Smale condition, the Morse relations hold. More precisely, let x ∈ M be a critical point of f , and m(x, f) denote the Morse index at x (i.e. the maximal dimension of the subspaces of TxM where the...
متن کاملMorse Theory , Floer Theory and Closed Geodesics of S
We construct Bott-type Floer homology groups for the sym-plectic manifold (T S 1 ; can) and Bott-type Morse homology groups for the energy functional on the loop space of S 1. Both objects turn out to be isomorpic to the singular homology of the loop space of S 1. So far our objects depend on all choices involved, but the above isomorphism suggests further investigation to show independence of ...
متن کاملA Morse complex for Lorentzian geodesics
We prove the Morse relations for all geodesics connecting two non-conjugate points on a class of globally hyperbolic Lorentzian manifolds. We overcome the difficulties coming from the fact that the Morse index of every geodesic is infinite, and from the lack of the Palais-Smale condition, by using the Morse complex approach. Introduction Let M be a smooth connected manifold without boundary of ...
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2014
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2014.v22.n5.a1