Odd Chern character in Hilbert A-module bundles

Let M be a compact manifold. Let W be a smooth Hilbert A-module bundle over M equipped with connection and curvature, where A is an unital C∗-algebra. After reviewing some literature, we are inspired that an analog of the odd Chern character form can be defined in the Hilbert A-module bundle setting...

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Bibliographic Details
Main Authors: Yu, Woon Le, Lim, Johnny
Format: Conference Proceeding
Language:English
Subjects:
Algebra
Homology
Modules
Online Access:Get full text
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Summary:Let M be a compact manifold. Let W be a smooth Hilbert A-module bundle over M equipped with connection and curvature, where A is an unital C∗-algebra. After reviewing some literature, we are inspired that an analog of the odd Chern character form can be defined in the Hilbert A-module bundle setting. In this paper, an explicit description of the odd Chern character form on W is provided via Getzler’s method through the Chern-Simons form. Then, the properties of the Chern-Simons form and the odd Chern character are provided under this setting. Lastly, a commutative diagram involving the K-theory with coefficients in C∗-algebra, K0(M × S1; A) and K1(M; A) is established and related to its associated cohomology group respectively.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0225492