Noncommutative Maslov Index And Eta Forms
Download Noncommutative Maslov Index And Eta Forms PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Noncommutative Maslov Index And Eta Forms book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Noncommutative Maslov Index and Eta-Forms
Author: Charlotte Wahl
language: en
Publisher: American Mathematical Soc.
Release Date: 2007
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.
Noncommutative Maslov Index and Eta-forms
Author: Charlotte Wahl
language: en
Publisher: American Mathematical Soc.
Release Date: 2007
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.
Index Theory, Eta Forms, and Deligne Cohomology
Author: Ulrich Bunke
language: en
Publisher: American Mathematical Soc.
Release Date: 2009-03-06
This paper sets up a language to deal with Dirac operators on manifolds with corners of arbitrary codimension. In particular the author develops a precise theory of boundary reductions. The author introduces the notion of a taming of a Dirac operator as an invertible perturbation by a smoothing operator. Given a Dirac operator on a manifold with boundary faces the author uses the tamings of its boundary reductions in order to turn the operator into a Fredholm operator. Its index is an obstruction against extending the taming from the boundary to the interior. In this way he develops an inductive procedure to associate Fredholm operators to Dirac operators on manifolds with corners and develops the associated obstruction theory.