| 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 |
| 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 128; 1997; 80 ppMSC: 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).
ReadershipGraduate students and research mathematicians interested in index theory; topologists and gauge theorists.
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Table of Contents
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Chapters
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1. Algebraic preliminaries
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2. Topological preliminaries
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3. $(p,q)$-lagrangians and classifying spaces for $K$-theory
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4. Symplectic reductions
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5. Clifford symmetric Fredholm operators
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6. Families of boundary value problems for Dirac operators
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Appendix A. Gap convergence of linear operators
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Appendix B. Gap continuity of families of BVP’s for Dirac operators
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Appendix C. Pseudodifferential Grassmanians and BVP’s for Dirac operators
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Appendix D. The proof of Proposition 6.1
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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).
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
