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Noncommutative Maslov Index and Eta-Forms
Charlotte Wahl, Virginia Polytechnic Institute and State University, Blacksburg, VA

Memoirs of the American Mathematical Society
2007; 118 pp; softcover
Volume: 189
ISBN-10: 0-8218-3997-7
ISBN-13: 978-0-8218-3997-3
List Price: US$67
Individual Members: US$40.20
Institutional Members: US$53.60
Order Code: MEMO/189/887
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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.

Table of Contents

  • Introduction
  • Preliminaries
  • The Fredholm operator and its index
  • Heat semigroups and kernels
  • Superconnections and the index theorem
  • Definitions and techniques
  • Bibliography
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