Noncommutative Maslov Index and Eta-Forms

Noncommutative Maslov Index and Eta-Forms
Author :
Publisher : American Mathematical Soc.
Total Pages : 130
Release :
ISBN-10 : 9780821839973
ISBN-13 : 0821839977
Rating : 4/5 (977 Downloads)

Book Synopsis Noncommutative Maslov Index and Eta-Forms by : Charlotte Wahl

Download or read book Noncommutative Maslov Index and Eta-Forms written by Charlotte Wahl and published by American Mathematical Soc.. This book was released on 2007 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


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