Hitchin-Thorpe Inequality for Noncompact Einstein 4-Manifolds

2006/12/04 by Xianzhe Dai, Dai, Xianzhe, Guofang Wei +1 · 1 citation
Mathematics · #53C #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C

paper · pdf · doi:10.48550/arxiv.math/0612105

17 pages

arxiv created 2006/12/04 · arxiv updated 2009/12/01

Abstract

We prove a Hitchin-Thorpe inequality for noncompact Einstein 4-manifolds with asymptotic geometry at infinity. The asymptotic geometry at infinity is either a cusp bundle over a compact space (the fibered cusps) or a fiber bundle over a cone with a compact fiber (the fibered boundary). Many noncompact Einstein manifolds come with such a geometry at infinity.

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