Produktdetaljer
<p><strong>Praise for Previous Editions:<br /></strong>...a very impressive book.<br />-<em>Australian and New Zealand Physicist</em></p>
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<p>The clarity of the presentation is enhanced by explicit calculations and diagrams ... There is also a large number of exercises and problems, and last but not least, an index ... superb layout...<br />-<em>Zentralblatt fur Mathematick</em></p>
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 Fiber 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