Morse theoretic methods in nonlinear analysis and in symplectic topology

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Morse theoretic methods in nonlinear analysis and in symplectic topology / edited by Paul Biran, Octav Cornea and François Lalonde

資料種別:

図書

出版情報:

Dordrecht : Springer, c2006

形態:

xiv, 462 p. ; 25 cm

シリーズ名:

NATO science series ; ser. 2 . Mathematics, physics and chemistry ; v. 217 <BA40559140>

著者名:

ISBN:

9781402042720 [1402042728]
9781402042737 [1402042736] (: PB)

書誌ID:

BA75520072

子書誌情報

フルテキスト

所蔵情報

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書誌詳細

注記:

"Published in cooperation with NATO Public Diplomacy Division."
"Proceeding of the NATO Advanced Study Institute on Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology, Montréal, Canada, July 2004."--T.p. verso
"Series II: Mathematics, physics and chemistry - vol. 216"--Facing t.p
Includes bibliographical references and index

主題:

Morse theory--Congresses; Symplectic and contact topology--Congresses

言語:

英語

目次情報:

Preface

Contributors

Lectures on the Morse Complex for Infinite-Dimensional Manifolds / A. Abbondandolo ; P. Majer

A few facts from hyperbolic dynamics / 1：

Adapted norms / 1.1：

Linear stable and unstable spaces of an asymptotically hyperbolic path / 1.2：

Morse vector fields / 1.3：

Local dynamics near a hyperbolic rest point / 1.4：

Local stable and unstable manifolds / 1.5：

The Grobman - Hartman linearization theorem / 1.6：

Global stable and unstable manifolds / 1.7：

The Morse complex in the case of finite Morse indices / 2：

The Palais - Smale condition / 2.1：

The Morse - Smale condition / 2.2：

The assumptions / 2.3：

Forward compactness / 2.4：

Consequences of compactness and transversality / 2.5：

Cellular filtrations / 2.6：

The Morse complex / 2.7：

Representation of delta in terms of intersection numbers / 2.8：

How to remove the assumption (A8) / 2.9：

Morse functions on Hilbert manifolds / 2.10：

Basic results in transversality theory / 2.11：

Genericity of the Morse - Smale condition / 2.12：

Invariance of the Morse complex / 2.13：

The Morse complex in the case of infinite Morse indices / 3：

The program / 3.1：

Fredholm pairs and compact perturbations of linear subspaces / 3.2：

Finite-dimensional intersections / 3.3：

Essential subbundles / 3.4：

Orientations / 3.5：

Compactness / 3.6：

Two-dimensional intersections / 3.7：

Bibliographical note / 3.8：

Notes on Floer Homology and Loop Space Homology / M. Schwarz

Introduction

Main result

Loop space homology

Floer homology for the cotangent bundle

Ring structures and ring-homomorphisms

The pair-of-pants product

The ring homomorphisms between free loop space Floer homology and based loop space Floer homology and classical homology

Morse-homology on the loop spaces Lambda and Omega, and the isomorphism / 4：

Products in Morse-homology / 5：

Ring isomorphism between Morse homology and Floer homology.- Homotopical Dynamics in Symplectic Topology / J.-F. Barraud ; O. Cornea5.1：

Elements of Morse theory

Connecting manifolds

Operations

Applications to symplectic topology

Bounded orbits

Detection of pseudoholomorphic strips and Hofer's norm.- Morse Theory, Graphs, and String Topology / R. L. Cohen

Graphs, Morse theory, and cohomology operations

String topology

A Morse theoretic view of string topology

Cylindrical holomorphic curves in the cotangent bundle.- Topology of Robot Motion Planning / M. Farber

First examples of configuration spaces

Varieties of polygonal linkages

Short and long subsets

PoincarF polynomial of M(a)

Universality theorems for configuration spaces

A remark about configuration spaces in robotics

The motion planning problem / 6：

Tame motion planning algorithms / 7：

The Schwarz genus / 8：

The second notion of topological complexity / 9：

Homotopy invariance / 10：

Order of instability of a motion planning algorithm / 11：

Random motion planningalgorithms / 12：

Equality theorem / 13：

An upper bound for TC(X) / 14：

A cohomological lower bound for TC(X) / 15：

Examples / 16：

Simultaneous control of many systems / 17：

Another inequality relating TC(X) to the usual category / 18：

Topological complexity of bouquets / 19：

A general recipe to construct a motion planning algorithm / 20：

How difficult is to avoid collisions in $ mathbb{R}$m? / 21：

The case m = 2 / 22：

TC(F($ mathbb{R}$m; n) in the case m $ geq$ 3 odd / 23：

Shade / 24：

Illuminating the complement of the braid arrangement / 25：

A quadratic motion planning algorithm in F($ mathbb{R}$m; n) / 26：

Configuration spaces of graphs / 27：

Motion planning in projective spaces / 28：

Nonsingular maps / 29：

TC(($ mathbb{R}$Pn) and the immersion problem / 30：

Some open problems.- Application of Floer Homology of Langrangian Submanifolds to Symplectic Topology / K. Fukaya31：

Lagrangian submanifold of $ mathbb{C}$n

Perturbing Cauchy - Riemann equation

Maslov index of Lagrangian submanifold with vanishing second Betti number

Floer ho

Preface

Contributors

Lectures on the Morse Complex for Infinite-Dimensional Manifolds / A. Abbondandolo ; P. Majer

A few facts from hyperbolic dynamics / 1：

Adapted norms / 1.1：

Linear stable and unstable spaces of an asymptotically hyperbolic path / 1.2：

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