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Generalized Symplectic Geometries and the Index of Families of Elliptic Problems
 
Liviu I. Nicolaescu University of Michigan, Ann Arbor
Generalized Symplectic Geometries and the Index of Families of Elliptic Problems
eBook ISBN:  978-1-4704-0194-8
Product Code:  MEMO/128/609.E
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $27.00
Generalized Symplectic Geometries and the Index of Families of Elliptic Problems
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Generalized Symplectic Geometries and the Index of Families of Elliptic Problems
Liviu I. Nicolaescu University of Michigan, Ann Arbor
eBook ISBN:  978-1-4704-0194-8
Product Code:  MEMO/128/609.E
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $27.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1281997; 80 pp
    MSC: Primary 58; 47; 55; Secondary 15; 16;

    In this book, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family.

    All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eight symmetries in the real case and two in the complex case).

    Readership

    Graduate students and research mathematicians interested in index theory; topologists and gauge theorists.

  • Table of Contents
     
     
    • Chapters
    • 1. Algebraic preliminaries
    • 2. Topological preliminaries
    • 3. $(p,q)$-lagrangians and classifying spaces for $K$-theory
    • 4. Symplectic reductions
    • 5. Clifford symmetric Fredholm operators
    • 6. Families of boundary value problems for Dirac operators
    • Appendix A. Gap convergence of linear operators
    • Appendix B. Gap continuity of families of BVP’s for Dirac operators
    • Appendix C. Pseudodifferential Grassmanians and BVP’s for Dirac operators
    • Appendix D. The proof of Proposition 6.1
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1281997; 80 pp
MSC: Primary 58; 47; 55; Secondary 15; 16;

In this book, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family.

All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eight symmetries in the real case and two in the complex case).

Readership

Graduate students and research mathematicians interested in index theory; topologists and gauge theorists.

  • Chapters
  • 1. Algebraic preliminaries
  • 2. Topological preliminaries
  • 3. $(p,q)$-lagrangians and classifying spaces for $K$-theory
  • 4. Symplectic reductions
  • 5. Clifford symmetric Fredholm operators
  • 6. Families of boundary value problems for Dirac operators
  • Appendix A. Gap convergence of linear operators
  • Appendix B. Gap continuity of families of BVP’s for Dirac operators
  • Appendix C. Pseudodifferential Grassmanians and BVP’s for Dirac operators
  • Appendix D. The proof of Proposition 6.1
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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