Analysis, Manifolds and Physics Part II

This second, companion volume contains 92 applications developing concepts and theorems presented or mentioned in the first volume. Introductions to and applications in several areas not previously covered are also included such as graded algebras with applications to Clifford algebras and (S)pin groups, Weyl Spinors, Majorana pinors, homotopy, supersmooth mappings and Berezin integration, Noether's theorems, homogeneous spaces with applications to Stiefel and Grassmann manifolds, cohomology with applications to (S)pin structures, Backlund transformations, Poisson manifolds, conformal transformations, Kaluza-Klein theories, Calabi-Yau spaces, universal bundles, bundle reduction and symmetry breaking, Euler-Poincare characteristics, Chern-Simons classes, anomalies, Sobolev embedding, Sobolev inequalities, Wightman distributions and Schwinger functions. The material included covers an unusually broad area and the choice of problems is guided by recent applications of differential geometry to fundamental problems of physics as well as by the authors' personal interests.