Noncommutative Maslov Index and Eta-Forms (eBook)

Charlotte Wahl (Autor)

eBook Download: PDF

118 Seiten
American Mathematical Society (Verlag)
9781470404918 (ISBN)

Infos

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.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-13: 9781470404918 / 9781470404918