**Memoirs of the American Mathematical Society**

2007;
118 pp;
Softcover

MSC: Primary 19;
Secondary 53; 58; 46

Print ISBN: 978-0-8218-3997-3

Product Code: MEMO/189/887

List Price: $67.00

AMS Member Price: $40.20

MAA Member Price: $60.30

**Electronic ISBN: 978-1-4704-0491-8
Product Code: MEMO/189/887.E**

List Price: $67.00

AMS Member Price: $40.20

MAA Member Price: $60.30

# Noncommutative Maslov Index and Eta-Forms

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*Charlotte Wahl*

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.