Spin geometry
Author(s)
Bibliographic Information
Spin geometry
(Princeton mathematical series, 38)
Princeton University Press, 1989
Available at / 90 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
LAW||3||6||複本200003622361
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC19:539.7/L4452070323730
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Note
Bibliography: p. 402-416
Includes indexes
Description and Table of Contents
Description
This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration.
A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds.
Table of Contents
*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. ix*Acknowledgments, pg. xii*Introduction, pg. 1*I. Clifford Algebras, Spin Groups and Their Representations, pg. 7*II. Spin Geometry and the Dirac Operators, pg. 77*III. Index Theorems, pg. 166*IV. Applications in Geometry and Topology, pg. 278*Appendix A. Principal G-Bundles, pg. 370*Appendix B. Classifying Spaces and Characteristic Classes, pg. 376*Appendix C. Orientation Classes and Thom Isomorphisms in K-Theory, pg. 384*Appendix D. Spin'-Manifolds, pg. 390*Bibliography, pg. 402*Index, pg. 417*Notation Index, pg. 425
by "Nielsen BookData"