Geometry, Topology and Physics, Third Edition (3^rd Ed.)

Covering recent developments in the field, this updated text provides an introduction to the ideas and techniques of differential geometry and topology. In this edition, the applications have been greatly expanded and additional problems have been included. The author examines anomalies in gauge field theories, bosonic string theory, Brane-World cosmology, Seiberg-Witten invariants, and topological quantum computing. A solutions manual is available for qualifying instructors.

FUNDAMENTALS: Quantum Physics. Mathematical Preliminaries. Homology Groups. Homotopy Groups. Knots, Links and Braids. de Rham Cohomology Groups. Riemannian Geometry. Complex Manifolds. Fiber Bundles. Connections on Fibre Bundles. Characteristic Classes. Index Theorems. APPLICATIONS: Anomalies in Gauge Field Theories. Bosonic String Theory. Brane-World Cosmology. Topological Aspects of Quantum Hall Effects and Topological Insulators. Topological Aspects of Quantum Computing. Seiberg·Witten Invariants and Topology of 4-Manifolds. Shape of the Universe. Poincare Conjecture and Ricci Flow.