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Febuary 2020 Elliptic operators and K-homology
Anna Duwenig
Rocky Mountain J. Math. 50(1): 91-124 (Febuary 2020). DOI: 10.1216/rmj.2020.50.91

Abstract

If a differential operator D on a smooth Hermitian vector bundle S over a compact manifold M is symmetric, it is essentially self-adjoint and so admits the use of functional calculus. If D is also elliptic, then the Hilbert space of square integrable sections of S with the canonical left C(M)-action and the operator χ(D) for χ a normalizing function is a Fredholm module, and its K-homology class is independent of χ. In this expository article, we provide a detailed proof of this fact following the outline in the book “Analytic K-homology” by Higson and Roe.

Citation

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Anna Duwenig. "Elliptic operators and K-homology." Rocky Mountain J. Math. 50 (1) 91 - 124, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.91

Information

Received: 3 May 2019; Revised: 27 August 2019; Accepted: 3 September 2019; Published: Febuary 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07201556
MathSciNet: MR4092546
Digital Object Identifier: 10.1216/rmj.2020.50.91

Subjects:
Primary: 19K33
Secondary: 46F12, 58-02

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
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Vol.50 • No. 1 • Febuary 2020
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