Generalized symplectic geometries and the index of families of elliptic problems
著者
書誌事項
Generalized symplectic geometries and the index of families of elliptic problems
（Memoirs of the American Mathematical Society, no. 609）
American Mathematical Society, 1997
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注記
"July 1997, volume 128, number 609 (first of 4 numbers)"
Includes bibliographical references (p. 78-80)
内容説明・目次
内容説明
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).
目次
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.
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