带有任意数域系数的负曲率轨道空间的贝蒂数
Betti Numbers of Negatively Curved Orbifolds with Coefficients in Arbitrary Fields
AI总结：
该研究证明了负曲率轨道空间的贝蒂数随体积线性增长，并扩展了格罗莫夫的定理至轨道空间，解决了萨梅特关于任意特征的问题。
摘要：
我们证明了有限体积负曲率轨道空间的贝蒂数随着体积的增长至多是线性的，无论系数在任意数域中。特别是，这为有限体积双曲轨道空间在$\mathbb{F}_p$上的贝蒂数提供了一个线性界。这扩展了格罗莫夫关于流形的定理到轨道空间在负曲率的情况，并回答了萨梅特的问题，通过将他的定理从特征0扩展到任意特征。关键的新输入是一个关于球面商的同调的定量界。
英文摘要：
We show that the Betti numbers of finite-volume negatively curved orbifolds grow at most linearly with the volume, with coefficients in an arbitrary field. In particular, this gives a linear bound for the Betti numbers of finite-volume hyperbolic orbifolds over $\mathbb{F}_p$. This extends a theorem of Gromov from manifolds to orbifolds in negative curvature, and answers a question of Samet, by strengthening his theorem from characteristic $0$ to arbitrary characteristic. The key new input is a quantitative bound on the homology of spherical quotients.
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