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# Noncommutative Maslov Index and Eta-Forms

ISBN-10: 0821839977

ISBN-13: 9780821839973

Pub. Date: 07/31/2007

Publisher: American Mathematical Society

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

## Overview

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.

## Product Details

ISBN-13:
9780821839973
Publisher:
American Mathematical Society
Publication date:
07/31/2007
Series:
Memoirs of the American Mathematical Society Series , #189
Pages:
118
Product dimensions:
6.90(w) x 10.00(h) x 0.30(d)

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