A note on the growth of Betti numbers and ranks of 3-manifold groups

2013/01/17 by Stefan Friedl, Friedl, Stefan
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1301.4025

10 pages, updated references

arxiv created 2013/04/18 · arxiv updated 2013/04/19

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 pi<sub>1</sub>(N) with `slow' growth of ranks.

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