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Noncommutative Maslov Index and Eta-Forms
 
Charlotte Wahl Virginia Polytechnic Institute and State University, Blacksburg, VA
Noncommutative Maslov Index and Eta-Forms
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
Noncommutative Maslov Index and Eta-Forms
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Noncommutative Maslov Index and Eta-Forms
Charlotte Wahl Virginia Polytechnic Institute and State University, Blacksburg, VA
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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1892007; 118 pp
    MSC: 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.

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1892007; 118 pp
MSC: 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.

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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