Orbifolds and Stringy Topology
Orbifolds and Stringy Topology by Alejandro Adem, published by Cambridge University Press on May 31, 2007, is an illustrated work comprising 164 pages in English. This book serves as an introduction to the theory of orbifolds, presenting a modern perspective that integrates techniques from geometry, algebraic topology, and algebraic geometry. It explores the classical description of orbifolds in relation to manifold theory and extends the discussion to include groupoid descriptions and examples within algebraic geometry, emphasizing the relevance of orbifolds in string theory.
Readers will find a thorough examination of classical invariants such as de Rham cohomology and bundle theory, alongside a careful analysis of orbifold morphisms and orbifold K-theory. The core of the text is dedicated to a detailed exploration of Chen-Ruan cohomology, which introduces a product for orbifolds and has had a significant impact on the field. The final chapter presents explicit computations for various interesting examples, making this work a valuable resource for those interested in the mathematical aspects of topology and its applications in theoretical physics.
Official synopsis Publisher
An introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry. One of the main motivations, and a major source of examples, is string theory, where orbifolds play an important role. The subject is first developed following the classical description analogous to manifold theory, after which the book branches out to include the useful description of orbifolds provided by groupoids, as well as many examples in the context of algebraic geometry. Classical invariants such as de Rham cohomology and bundle theory are developed, a careful study of orbifold morphisms is provided, and the topic of orbifold K-theory is covered. The heart of this book, however, is a detailed description of the Chen-Ruan cohomology, which introduces a product for orbifolds and has had significant impact. The final chapter includes explicit computations for a number of interesting examples.
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