New Lower Bounds on Subgroup Growth and Homology Growth
نویسنده
چکیده
Subgroup growth is an important new area of group theory. It attempts to quantify the number of finite index subgroups of a group, as a function of their index. In this paper, we will provide new, strong lower bounds on the subgroup growth of a variety of different groups. This will include the fundamental groups of all finite-volume hyperbolic 3-manifolds. By using the correspondence between subgroups and covering spaces, we will be able to address the following natural question: how many finite-sheeted covering spaces does a hyperbolic 3-manifold have, as a function of the covering degree?
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