By Edward R. Fadell

The configuration area of a manifold offers the proper environment for difficulties not just in topology but additionally in different parts comparable to nonlinear research and algebra. With functions in brain, the purpose of this monograph is to supply a coherent and thorough therapy of the configuration areas of Eulidean areas and spheres which makes the topic available to researchers and graduate scholars with a minimum historical past in classical homotopy idea and algebraic topology. The remedy regards the homotopy relatives of Yang-Baxter kind as being primary. it is also a unique and geometric presentation of the classical natural braid team; the mobile constitution of those configuration areas which results in a mobile version for the linked dependent and unfastened loop areas; the homology and cohomology of established and loose loop areas; and a demonstration of ways to use the latter to the research of Hamiltonian platforms of k-body type.