The discovery of on-standard smoothness structures on topologically trivial manifolds promises new paths of research in space-time models of theoretical physics, particularly in general relativity. Asselmeyer-Maluga (physics, the Fraunhofer Institute) and Brans (theoretical physics, Loyola U.) introduce some of the developments in the mathematics of differential topology, in particular the non-standard ("exotic") smoothness on topologically simple spaces. They introduce the basics, such as the interaction of physics and mathematics, and the characteristics of basic topological exotica, then explain the algebraic tools for topology, the geometry of smooth folds, the relations between bundles and geometry with gauge theory, the relations between gauge theory and moduli space, the classification of manifolds, early exotic manifolds, the first results in dimension four, the modern approach to the Seiberg-Witten theory, physical implications, and the move from differential structures to operator algebras and geometric structures. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)
