With applications in mind, this self-contained monograph provides a coherent and thorough treatment of the configuration spaces of Euclidean spaces and spheres, making the subject accessible to researchers and graduates with a minimal background in classical homotopy theory and algebraic topology.
Part 1: The Homotopy of Configuration Spaces.Basic Fibrations.Configuration space of Euclidean Space.Configuration spaces on spheres. The two-dimensional case.Part 2: The cohomology algebra of configuration spaces.Cellular models. Cellular chain models.Part 3: The Homology of Based LoopsRPT-Constructions. Cellular chain algebra modelsThe Serre spectral sequenceComputation of the homology of the free loop spaceEnds and Gamma categoryAn application to problems of k-body type.