Open Access
January 2014 The harmonic field of a Riemannian manifold
Steve Halperin
J. Differential Geom. 96(1): 61-76 (January 2014). DOI: 10.4310/jdg/1391192692


Sullivan’s construction of minimal models for topological spaces is refined for the case of a simply connected closed Riemannian manifold, $(M,\lt,\gt)$, to define a unique finitely generated field extension, $\mathbf{k}$ of $\mathbf{Q}$, baptized the harmonic field of $(M,\lt,\gt)$, and a morphism, $m:(\Lambda V,d)\rightarrow A_{DR}(M)$, from a Sullivan model defined over $\mathbf{k}$. The Sullivan model and the morphism are determined up to isomorphism, and the natural extension of $H(m)$ to $H(\Lambda V,d)\otimes_{\mathbf{k}}\mathbf{R}$ is an isomorphism; in particular, $(\Lambda V,d)$ is isomorphic to a rational Sullivan model for $M$ tensored with $\mathbf{k}$. Examples are constructed to show that every finitely generated extension field of $\mathbf{Q}$ occurs as a harmonic field of such a Riemannian manifold.


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Steve Halperin. "The harmonic field of a Riemannian manifold." J. Differential Geom. 96 (1) 61 - 76, January 2014.


Published: January 2014
First available in Project Euclid: 31 January 2014

zbMATH: 1310.53032
MathSciNet: MR3161385
Digital Object Identifier: 10.4310/jdg/1391192692

Rights: Copyright © 2014 Lehigh University

Vol.96 • No. 1 • January 2014
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