Singular surfaces, mod 2 homology, and hyperbolic volume, II

Details Singular surfaces, mod 2 homology, and hyperbolic volume, II Singular surfaces, mod 2 homology, and hyperbolic volume, II

2007-01-24

arxiv.org/abs/math/0701666v7

Mathematics

Geometric Topology

23 pages. This version incorporates suggestions from the referee and adds a new section giving examples showing that the main

Scientific paper

If M is a closed simple 3-manifold whose fundamental group contains a genus-g surface group for some g>1, and if the dimension of H_1(M;Z_2) is at least max(3g-1,6), we show that M contains a closed, incompressible surface of genus at most g. This improves the main topological result of part I, in which the the same conclusion was obtained under the stronger hypothesis that the dimension of H_1(M;Z_2) is at least 4g-1. As an application we show that if M is a closed orientable hyperbolic 3-manifold with volume at most 3.08, then H_1(M;Z_2) has dimension at most 5.

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