Cusp and b1 growth for ball quotients and maps onto Z with finitely generated kernel
نویسنده
چکیده
Let M = B/Γ be a smooth ball quotient of finite volume with first betti number b1(M) and let E(M) ≥ 0 be the number of cusps (i.e., topological ends) of M . We study the growth rates that are possible in towers of finite-sheeted coverings of M . In particular, b1 and E have little to do with one another, in contrast with the well-understood cases of hyperbolic 2and 3-manifolds. We also discuss growth of b1 for congruence arithmetic lattices acting on B and B. Along the way, we provide an explicit example of a lattice in PU(2, 1) admitting a homomorphism onto Z with finitely generated kernel. Moreover, we show that any cocompact arithmetic lattice Γ ⊂ PU(n, 1) of simplest type contains a finite index subgroup with this property.
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تاریخ انتشار 2016