A Burns-Epstein invariant for ACHE 4-manifolds

2001/11/20 by Olivier Biquard, Biquard, Olivier, Marc Herzlich +1 · 1 citation
Mathematics · #53C55 #58J37 #58J60 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory #math.DG #msc:53C55 #msc:58J37 #msc:58J60

paper · pdf · doi:10.48550/arxiv.math/0111218

Lemma 2.6 changed because of a mistake. Section 5 (using lemma 2.6) rewritten

openalex publication_date 2001/11/20 · arxiv created 2002/10/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 euler-3signature is shown to converge. This extends a work of Burns and Epstein in the Kahler-Einstein case. This extends a work of Burns and Epstein in the Kahler-Einstein case. We also define a new global invariant for any 3-dimensional pseudoconvex CR manifold, by a renormalization procedure of the eta invariant of a sequence of metrics which approximate the CR structure. Finally, we get a formula relating the renormalized characteristic class to the topological number euler-3signature and the invariant of the CR structure arising at infinity.

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