# A Bakry–Émery Almost Splitting Result With Applications to the Topology of Black Holes

@article{Galloway2020ABA, title={A Bakry–{\'E}mery Almost Splitting Result With Applications to the Topology of Black Holes}, author={Gregory J. Galloway and Marcus A. Khuri and Eric Woolgar}, journal={arXiv: Differential Geometry}, year={2020} }

The almost splitting theorem of Cheeger-Colding is established in the setting of almost nonnegative generalized $m$-Bakry-Emery Ricci curvature, in which $m$ is positive and the associated vector field is not necessarily required to be the gradient of a function. In this context it is shown that with a diameter upper bound and volume lower bound the fundamental group of such manifolds is almost abelian. Furthermore, extensions of well-known results concerning Ricci curvature lower bounds are… Expand

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