| eBook ISBN: | 978-1-4704-0491-8 |
| Product Code: | MEMO/189/887.E |
| List Price: | $67.00 |
| MAA Member Price: | $60.30 |
| AMS Member Price: | $40.20 |
| eBook ISBN: | 978-1-4704-0491-8 |
| Product Code: | MEMO/189/887.E |
| List Price: | $67.00 |
| MAA Member Price: | $60.30 |
| AMS Member Price: | $40.20 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 189; 2007; 118 ppMSC: Primary 19; Secondary 53; 58; 46
The author defines and proves a noncommutative generalization of a formula relating the Maslov index of a triple of Lagrangian subspaces of a symplectic vector space to eta-invariants associated to a pair of Lagrangian subspaces. The noncommutative Maslov index, defined for modules over a \(C^*\)-algebra \(\mathcal{A}\), is an element in \(K_0(\mathcal{A})\).
The generalized formula calculates its Chern character in the de Rham homology of certain dense subalgebras of \(\mathcal{A}\). The proof is a noncommutative Atiyah-Patodi-Singer index theorem for a particular Dirac operator twisted by an \(\mathcal{A}\)-vector bundle. The author develops an analytic framework for this type of index problem.
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Table of Contents
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Chapters
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Introduction
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1. Preliminaries
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2. The Fredholm operator and its index
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3. Heat semigroups and kernels
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4. Superconnections and the index theorem
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5. Definitions and techniques
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The author defines and proves a noncommutative generalization of a formula relating the Maslov index of a triple of Lagrangian subspaces of a symplectic vector space to eta-invariants associated to a pair of Lagrangian subspaces. The noncommutative Maslov index, defined for modules over a \(C^*\)-algebra \(\mathcal{A}\), is an element in \(K_0(\mathcal{A})\).
The generalized formula calculates its Chern character in the de Rham homology of certain dense subalgebras of \(\mathcal{A}\). The proof is a noncommutative Atiyah-Patodi-Singer index theorem for a particular Dirac operator twisted by an \(\mathcal{A}\)-vector bundle. The author develops an analytic framework for this type of index problem.
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Chapters
-
Introduction
-
1. Preliminaries
-
2. The Fredholm operator and its index
-
3. Heat semigroups and kernels
-
4. Superconnections and the index theorem
-
5. Definitions and techniques
