Geometry and Topology of Configuration Spaces
By: by Edward R. Fadell, Sufian Y. Husseini
Contributors: Husseini, Sufian Y.
Series: Springer Monographs in Mathematics; Springer monographs in mathematics
Publisher: Springer Berlin Heidelberg
Published: 2001
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 313
ISBN-13: 9783642630774; 9783642564468
Subjects: Mathematics; Algebraic topology; Global analysis
Description: The configuration space of a manifold provides the appropriate setting for problems not only in topology but also in other areas such as nonlinear analysis and algebra. With applications in mind, the aim of this monograph is to provide a coherent and thorough treatment of the configuration spaces of Eulidean spaces and spheres which makes the subject accessible to researchers and graduate students with a minimal background in classical homotopy theory and algebraic topology. The treatment regards the homotopy relations of Yang-Baxter type as being fundamental. It also includes a novel and geometric presentation of the classical pure braid group; the cellular structure of these configuration spaces which leads to a cellular model for the associated based and free loop spaces; the homology and cohomology of based and free loop spaces; and an illustration of how to apply the latter to the study of Hamiltonian systems of k-body type.
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Table of contents: title: Part 1: The Homotopy of Configuration Spaces. Basic Fibrations. Configuration space of Euclidean Space. Configuration spaces on spheres. The two-dimensional case; title: Part 2: The cohomology algebra of configuration spaces. Cellular models. Cellular chain models; title: Part 3: The Homology of Based Loops. RPT-Constructions. Cellular chain algebra models. The Serre spectral sequence. Computation of the homology of the free loop space. Ends and Gamma category. An application to problems of k-body type.