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Liviu I. Nicolaescu
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دانلود کتاب Generalized symplectic geometries and the index of families of elliptic problems
by Liviu I. Nicolaescu|
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عنوان فارسی: هندسه ها symplectic منتشر و شاخص خانواده از مشکلات بیضوی |
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جزییات کتاب
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).
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