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25 Remote Warehouse Physics- Nuclear

Princeton Mathematical Series #0038: Spin Geometry (PMS-38)

by

Princeton Mathematical Series #0038: Spin Geometry (PMS-38) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Book News Annotation:

The authors are professors of mathematics at Stony Brook. Their objective in the present monograph is to provide mature readers with an up to date review of ideas which (as they point out) originate in the relativistic physics of Dirac (1928) but, as deepened by M. Atiyah and I. Singer in the 1960s, have produced a rich fusion of topology, geometry and analysis which is today the locus of excited dialogue between mathematicians and physicists. Four dense chapters and as many appendices, very attractively typeset and produced. (NW)
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

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.

Product Details

ISBN:
9780691085425
Editor:
Michelsohn, Marie-Louise
Author:
Michelsohn, Marie-Louise
Author:
on, H. Blaine
Author:
Lawson, H. Blaine
Author:
Laws
Publisher:
Princeton University Press
Location:
Princeton, N.J. :
Subject:
Mathematics
Subject:
Geometry
Subject:
Advanced
Subject:
Nuclear Physics
Subject:
Mathematical Physics
Subject:
Topology
Subject:
Nuclear spin
Subject:
Clifford algebras
Subject:
Nuclear spin -- Mathematics.
Subject:
Spin geometry
Subject:
Geometry - Algebraic
Subject:
Physics-Nuclear
Copyright:
Edition Description:
Bibliography: p. 402-416.
Series:
Princeton Mathematical Series
Series Volume:
0038
Publication Date:
February 1990
Binding:
HARDCOVER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Yes
Pages:
440
Dimensions:
9.56x6.40x1.30 in. 1.60 lbs.

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Princeton Mathematical Series #0038: Spin Geometry (PMS-38) New Hardcover
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$172.50 In Stock
Product details 440 pages Princeton University Press - English 9780691085425 Reviews:
"Synopsis" by , 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.
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