Translator Disclaimer
15 January 2005 A Burns-Epstein invariant for ACHE 4-manifolds
Olivier Biquard, Marc Herzlich
Duke Math. J. 126(1): 53-100 (15 January 2005). DOI: 10.1215/S0012-7094-04-12612-0

Abstract

We define a renormalized characteristic class for Einstein asymptotically complex hyperbolic (ACHE) manifolds of dimension 4: for any such manifold, the polynomial in the curvature associated to the characteristic class χ−3τ is shown to converge. This extends a work of Burns and Epstein in the Kähler-Einstein case

We also define a new global invariant for any compact 3-dimensional strictly pseudoconvex Cauchy-Riemann (CR) manifold by a renormalization procedure of the η-invariant of a sequence of metrics that approximate the CR structure.

Finally, we get a formula relating the renormalized characteristic class to the topological number χ−3τ and the invariant of the CR structure arising at infinity.

Citation

Download Citation

Olivier Biquard. Marc Herzlich. "A Burns-Epstein invariant for ACHE 4-manifolds." Duke Math. J. 126 (1) 53 - 100, 15 January 2005. https://doi.org/10.1215/S0012-7094-04-12612-0

Information

Published: 15 January 2005
First available in Project Euclid: 15 December 2004

zbMATH: 1074.53037
MathSciNet: MR2110628
Digital Object Identifier: 10.1215/S0012-7094-04-12612-0

Subjects:
Primary: 53C55, 58J37, 58J60
Secondary: 32V15, 58J28

Rights: Copyright © 2005 Duke University Press

JOURNAL ARTICLE
48 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.126 • No. 1 • 15 January 2005
Back to Top