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Febuary 2020 Topological $K$-theory with coefficients and the $e$-invariant
Yi-Sheng Wang
Rocky Mountain J. Math. 50(1): 281-318 (Febuary 2020). DOI: 10.1216/rmj.2020.50.281

Abstract

We compare the invariants of flat vector bundles defined by Atiyah et al. and Jones et al. and prove that, up to weak homotopy, they induce the same map from the 0-connective algebraic K-theory space of the complex numbers to the homotopy fiber of the Chern character. We examine homotopy properties of this map and its relation with other known invariants. In addition, using the formula for ξ̃-invariants of lens spaces derived from Donnelly’s fixed point theorem and the 4-dimensional cobordisms constructed via relative Kirby diagrams, we recover the formula of the e-invariants of Seifert homology spheres given by Jones and Westbury, up to sign.

Citation

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Yi-Sheng Wang. "Topological $K$-theory with coefficients and the $e$-invariant." Rocky Mountain J. Math. 50 (1) 281 - 318, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.281

Information

Received: 29 April 2019; Accepted: 24 August 2019; Published: Febuary 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07201568
MathSciNet: MR4092558
Digital Object Identifier: 10.1216/rmj.2020.50.281

Subjects:
Primary: 19E20, 19L64

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 1 • Febuary 2020
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