A Burns-Epstein invariant for ACHE 4-manifolds

Details A Burns-Epstein invariant for ACHE 4-manifolds A Burns-Epstein invariant for ACHE 4-manifolds

2001-11-20

arxiv.org/abs/math/0111218v4

Mathematics

Differential Geometry

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

Scientific paper

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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