Generalized Symplectic Geometries and the Index of Families of Elliptic Problems
Liviu I. Nicolaescu
Jan 1997 · American Mathematical Society: Memoirs of the American Mathematical Society Book 609 · American Mathematical Soc.
Ebook
80
Pages
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About this ebook
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 (eigh symmetries in the real case and two in the complex case). This text will also be of interest to those working in geometry and topology.
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