Generalized Symplectic Geometries and the Index of Families of Elliptic-problems
Seiten
1997
American Mathematical Society (Verlag)
978-0-8218-0621-0 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-0621-0 (ISBN)
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Proves an index theorem 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. This work also obtains a general result on the cobordism invariance of the index of a family.
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).
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).
Algebraic preliminaries Topological preliminaries (p-q)-lagrangians and classifying spaces for K-theory Symplectic reductions Clifford Symmetric Fredholm operators Families of boundary value problems for Dirac operators Appendices References.
| Erscheint lt. Verlag | 30.8.1997 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 185 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-8218-0621-1 / 0821806211 |
| ISBN-13 | 978-0-8218-0621-0 / 9780821806210 |
| Zustand | Neuware |
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