Charlotte Wahl 
Noncommutative Maslov Index and Eta-Forms [PDF ebook] 

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.