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A Burns-Epstein invariant for ACHE 4-manifolds

Olivier Biquard·Marc Herzlich
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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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Olivier Biquard, Marc Herzlich. 2002-10-04. A Burns-Epstein invariant for ACHE 4-manifolds. https://arxiv.org/abs/math/0111218

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