On the topology of conformally compact Einstein 4-manifolds

Chang, Alice; Qing, Jie; Yang, Paul

On the topology of conformally compact Einstein 4-manifolds

Authors

Chang, Alice

Qing, Jie

Yang, Paul

Description

In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also positive we show that the conformally compact Einstein 4-manifold will have at most finite fundamental group. Under the further assumption that the renormalized volume is relatively large, we conclude that the conformally compact Einstein 4-manifold is diffeomorphic to $B^4$ and its conformal infinity is diffeomorphic to $S^3$.
16 pages