Memoirs of the American Mathematical Society 2007; 118 pp; softcover Volume: 189 ISBN10: 0821839977 ISBN13: 9780821839973 List Price: US$67 Individual Members: US$40.20 Institutional Members: US$53.60 Order Code: MEMO/189/887
 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 etainvariants 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 AtiyahPatodiSinger 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
