A note on the growth of Betti numbers and ranks of 3-manifold groups
Abstract
Let N be an irreducible, compact 3-manifold with empty or toroidal boundary which is not a closed graph manifold. Using recent work of Agol, Kahn-Markovic and Przytycki-Wise we will show that pi1(N) admits a cofinal filtration with `fast' growth of Betti numbers as well as a cofinal filtration of pi1(N) with `slow' growth of ranks.
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