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.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Gewicht
ISBN-13
978-0-8218-3997-3 (9780821839973)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Introduction Preliminaries The Fredholm operator and its index Heat semigroups and kernels Superconnections and the index theorem Definitions and techniques Bibliography.
