论文标题
双曲线轨道的同源界限
Homology bounds for hyperbolic orbifolds
论文作者
论文摘要
我们将在双曲线轨道的同源性的Betti数字和扭转部分上提供界限。这些边界在体积中是线性的，是厚部分有效的简单模型的直接结果，我们也将构建。同源性陈述补充了Bader，Gelander和Sauer的先前工作（歧管的扭转同源性），Samet（Orbifolds的Betti数字）和Gromov的经典定理（bitti歧管数字）。 对于算术，非紧凑双曲线孔 - 即，对于$ \ operatatorName {isom}（\ Mathbb {h}^n）$中的算术，不均匀的晶格，将获得最强的结果。
We will provide bounds on both the Betti numbers and the torsion part of the homology of hyperbolic orbifolds. These bounds are linear in the volume and are a direct consequence of an efficient simplicial model of the thick part, which we will construct as well. The homology statements complement previous work of Bader, Gelander and Sauer (torsion homology of manifolds), Samet (Betti numbers of orbifolds) and a classical theorem of Gromov (Betti numbers of manifolds). For arithmetic, non-compact hyperbolic orbifolds -- i.e. in the case of arithmetic, non-uniform lattices in $\operatorname{Isom}(\mathbb{H}^n)$ -- the strongest results will be obtained.
