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Spin Geometry. (PMS-38)

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H. Blaine Lawson (Author)
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H. Blaine Lawson (Author), Marie-Louise Michelsohn (Author)
4.5 out of 5 stars 2 customer reviews
ISBN-13: 978-0691085425
ISBN-10: 0691085420
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Product Details

  • Series: Princeton Mathematical Series (Book 38)
  • Hardcover: 427 pages
  • Publisher: Princeton University Press (February 1, 1990)
  • Language: English
  • ISBN-10: 0691085420
  • ISBN-13: 978-0691085425
  • Product Dimensions: 6.1 x 1 x 9.2 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #1,525,217 in Books (See Top 100 in Books)

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4.0 out of 5 starsEssential for grad students in geometry/topology
By Kevin M. Iga on December 22, 1998
Format: Hardcover
As a graduate student in mathematics I survived on this encyclopedic work. Anyone interested in differential geometry or differential topology will eventually need something in this book.
Prerequisites are graduate-level algebra and analysis, and some topology and differential geometry. He introduces the subject of pseudodifferential operators and Sobolev spaces, but it's easy to get lost in that part unless you first read Shubin's book "Pseudodifferential operators and Spectral theory". Also, the quick shuffling of Lie group information can be disheartening if you're not used to it. Harvey's book "Spinors and Calibrations" is a more elementary book if this is the case.
This book touches on many important topics like the Atiyah-Singer Index Theorem, the Bochner method, Riemann-Roch, and mathematical physics, but you will probably want to supplement your reading with individual books on each of these topics.
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5.0 out of 5 starsExcellent
By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on December 22, 2001
Format: Hardcover
Who would have known that the equation discovered by P.A.M. Dirac in the 1920's would have the enormous appllications to mathematics that it currently has. This book is an excellent overview of these applications, written by two individuals who are responsible for the development of many of these. Dirac's theory of course had its origins in physics, and physicists, particularly those working in high energy physics, will find this book interesting and helpful.
The authors give a brief introduction and then move on to the representation theory of Clifford algebras and spin groups in chapter 1. The reader can see the origin of Clifford algebras and an introduction to the Pin and Spin groups. Clifford algebras are classified as matrix algebras over the real or complex numbers, and the quaternions. It is the representation theory of Clifford algebras however that has resulted in the impressive results outlined in the book Noting that the tensor product of Clifford algebras is not necessarily a Clifford algebra, the authors introduce a Z(2)-grading on a Clifford algebra, which results in a multiplicative structure in the representations of Clifford algebras. The Lie algebras of the Pin and Spin groups are discussed along with applications to geometry and Lie groups. By far the most interesting discussion though is on K-theory, which allows one to define a ring structure on vector bundles. Distinguishing a base point in the base space, relative K-groups are defined, and shown to be equal for the base space and its i-fold suspension. Bott periodicity results are stated but their proof is delayed until chapter 3. A detailed discussion is given of the Atiyah-Bott-Shapiro isomorphism and KR-theory.
The connection between spin and differential geometry is discussed in chapter 2.Read more ›
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