Differential Geometry for Physicists (Advanced Series on Theoretical Physical Science)

This book provides an introduction to prerequisite topological and algebraic knowledge. The first seven chapters, focusing on local analysis, can be used as a fundamental textbook for graduate students of theoretical physics. The later chapters discuss geometry in fibre bundles, and deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry. The text aims to provide coverage of current research in theoretical physics.