m at h . G T ] 2 3 M ay 2 00 8 SINGULAR SURFACES , MOD 2 HOMOLOGY , AND HYPERBOLIC VOLUME , II
نویسنده
چکیده
If g is an integer ≥ 2, and M is a closed simple 3-manifold such that π1(M) has a subgroup isomorphic to a genus-g surface group and dimZ2 H1(M ;Z2) ≥ max(3g−1, 6), we show that M contains a closed, incompressible surface of genus at most g. As an application we show that if M is a closed orientable hyperbolic 3-manifold such that VolM ≤ 3.08, then dimZ2 H1(M ;Z2) ≤ 5.
منابع مشابه
2 3 A ug 2 00 7 SINGULAR SURFACES , MOD 2 HOMOLOGY , AND HYPERBOLIC VOLUME , II
The main theorem of this paper states that ifM is a closed orientable hyperbolic 3-manifold of volume at most 3.08, then the dimension of H1(M ;Z2) is at most 7, and that it is at most 6 unless M is “strange.” To say that a closed, orientable 3-manifold M , for which H1(M ;Z2) has dimension 7, is strange means that the Z2-vector space H1(M ;Z2) has a 2-dimensional subspace X such that for every...
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