Geometry and Topology of Configuration Spaces

The configuration space of a manifold provides the appropriate setting forproblems not only in topology but also in other areas such as nonlinearanalysis and al... » 

The configuration space of a manifold provides the appropriate setting forproblems not only in topology but also in other areas such as nonlinearanalysis and algebra. With applications in mind the aim of this monograph isto provide a coherent and thorough treatment of the configuration spaces ofEuclidean spaces and spheres which makes the subject accessible to researchersand graduate students with a minimal background in classical homotopy theoryand algebraic topology. The treatment regards the homotopy relations of YangBaxter type as being fundamental. It also includes a novel and geometricpresentation of the classical pure braid group the cellular structure of theseconfiguration spaces which leads to a cellular model for the associated basedand free loop spaces the homology and cohomology of based and free loopspaces and an illustration of how to apply the latter to the study ofHamiltonian systems of kbody type. «