Morse Theoretic Methods in Nonlinear Analysis And in Symplectic Topology (Hardcover)

'Preface.Contributors. Lectures on the Morse Complex for Infinite-Dimensional Manifolds; A. Abbondandolo and P. Majer.-1. A few facts from hyperbolic dynamics.-1.1 Adapted norms .-1.2 Linear stable and unstable spaces of an asymptotically hyperbolic path.-1.3 Morse vector fields.- 1.4 Local dynamics near a hyperbolic rest point ; 1.5 Local stable and unstable manifolds.- 1.6 The Grobman - Hartman linearization theorem.-1.7 Global stable and unstable manifolds.- 2 The Morse complex in the case of finite Morse indices.- 2.1 The Palais - Smale condition.-2.2 The Morse - Smale condition .-2.3 The assumptions .- 2.4 Forward compactness.- 2.5 Consequences of compactness and transversality.- 2.6 Cellular filtrations.- 2.7 The Morse complex.- 2.8 Representation of $\delta$ in terms of intersection numbers.- 2.9 How to remove the assumption (A8).- 2.10 Morse functions on Hilbert manifolds.-2.11 Basic results in transversality theory .- 2.12 Genericity of the Morse - Smale condition.-2.13 Invariance of the Morse complex.- 3 The Morse complex in the case of infinite Morse indices.- 3.1 The program.-3.2 Fredholm pairs and compact perturbations of linear subspaces.- 3.3 Finite-dimensional intersections.-3.4 Essential subbundles.- 3.5 Orientations.- 3.6 Compactness .- 3.7 Two-dimensional intersections .-3.8 The Morse complex.- Bibliographical note.- Notes on Floer Homology and Loop Space Homology; A. Abbondandolo and M. Schwarz.- 1 Introduction.- 2 Main result.-2.1 Loop space homology.-2.2 Floer homology for the cotangent bundle.- 3 Ring structures and ring-homomorphisms.-3.1 The pair-of-pants product.- 3.2 The ring homomorphisms between free loop space Floer homology and based loop space Floer homology and classical homology.-4 Morse-homology on the loop spaces $\Lambda$Q and $\Omega$Q, and the isomorphism.-5 Products in Morse-homology .-5.1 Ring isomorphism between Morse homology and Floer homology.- Homotopical Dynamics in Symplectic Topology; J.-F. Barraud and O. Cornea.- 1 Introduction .-2 Elements of Morse theory .-2.1 Connecting manifolds.-2.2 Operations.-3 Applications to symplectic topology.- 3.1 Bounded orbits .-3.2 Detection of pseudoholomorphic strips and Hofer's norm.- Morse Theory, Graphs, and String Topology; R. L. Cohen.-1 Graphs, Morse theory, and cohomology operations.-2 String topology .-3 A Morse theoretic view of string topology.- 4 Cylindrical holomorphic curves in the cotangent bundle.- Topology of Robot Motion Planning; M. Farber.-1.Introduction .-2 First examples of configuration spaces .-3 Varieties of polygonal linkages.-3.1 Short and long subsets .-3.2 Poincare polynomial of M(a) .-4 Universality theorems for configuration spaces .-5 A remark about configuration spaces in robotics .-6 The motion planning problem.-7 Tame motion planning algorithms.-8 The Schwarz genus.- 9 The second notion of topological complexity.-10 Homotopy invariance.- 11 Order of instability of a motion planning algorithm.-12 Random motion planning algorithms.- 13 Equality theorem.-14 An upper bound for TC(X).-15 A cohomological lower bound for TC(X) .-16 Examples .-17 Simultaneous control of many systems.-18 Another inequality relating TC(X) to the usual category .-19 Topological complexity of bouquets.-20 A general recipe to construct a motion planning algorithm.-21 How difficult is to avoid collisions in $\mathbb{R}$ m ? .-22 The case m = 2.- 23 TC(F($\mathbb{R}$ m ; n) in the case m $\geq$ 3 odd .- 24 Shade.-25 Illuminating the complement of the braid arrangement .-26 A quadratic motion planning algorithm in F($\mathbb{R}$ m ; n).-27 Configuration spaces of graphs.-28 Motion planning in projective spaces .-29 Nonsingular maps.- 30 TC(($\mathbb{R}$P n ) and the immersion problem.-31 Some open problems.- Application of Floer Homology of Langrangian Submanifolds to Symplectic Topology;K. Fukaya.- 1 Introduction.- 2 Lagrangian submanifold of $\