Noncommutative Maslov Index and Eta-forms

Charlotte Wahl (Autor)

Buch | Softcover

118 Seiten

2007
American Mathematical Society (Verlag)
9780821839973 (ISBN)

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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 author develops an analytic framework for this type of index problem.

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.

Introduction Preliminaries The Fredholm operator and its index Heat semigroups and kernels Superconnections and the index theorem Definitions and techniques Bibliography.

Erscheint lt. Verlag	1.9.2007
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Gewicht	239 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-13	9780821839973 / 9780821839973
Zustand	Neuware