Ju n 20 05 Singular surfaces , mod 2 homology , and hyperbolic volume , I
نویسنده
چکیده
The main theorem of this paper states that if M is a closed orientable hyperbolic 3-manifold such that the rank of H1(M ;Z/2Z) is at least 11, then VolM > 3.08. The theorem depends on a purely topological result which can be viewed as an analogue of Dehn’s lemma for π1-injective singular surfaces of genus 2. The proof of the main theorem combines this topological result with several deep geometric results, including the Marden tameness conjecture, recently established by Agol and by Calegari-Gabai; a co-volume estimate for 3-tame, 3-free Kleinian groups due to Anderson, Canary, Culler and Shalen; and a volume estimate for hyperbolic Haken manifolds recently proved by Agol, Storm and Thurston
منابع مشابه
20 07 Singular Surfaces , Mod 2 Homology , and Hyperbolic Volume , I
The main theorem of this paper states that ifM is a closed orientable hyperbolic 3-manifold of volume at most 3.08, then the rank ofH1(M ;Z/2Z) is at most 10. The theorem depends on a purely topological result which can be viewed as an analogue of Dehn’s lemma for π1-injective singular surfaces of genus 2. The proof of the main theorem combines this topological result with several deep geometri...
متن کاملSingular Surfaces, Mod 2 Homology, and Hyperbolic Volume, I
The main theorem of this paper states that if M is a closed orientable hyperbolic 3-manifold of volume at most 3.08, then the rank of H1(M ;Z/2Z) is at most 10. The theorem depends on a purely topological result which can be viewed as an analogue of Dehn’s lemma for π1-injective singular surfaces of genus 2. The proof of the main theorem combines this topological result with several deep geomet...
متن کاملSingular Surfaces , Mod 2 Homology , and Hyperbolic Volume
If M is a simple, closed, orientable 3-manifold such that π1(M) contains a genus-g surface group, and if H1(M ;Z2) has rank at least 4g−1, we show that M contains an embedded closed incompressible surface of genus at most g. As an application we show that if M is a closed orientable hyperbolic 3-manifold of volume at most 3.08, then the rank of H1(M ;Z2) is at most 6.
متن کامل2 4 Ja n 20 07 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...
متن کاملJu n 20 06 EULER HOMOLOGY
We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring N∗(X) of a topological space X. This homology theory Eh∗ has coefficients Z/2 in every nonnegative dimension. There exists a natural transformation N∗(X) → Eh∗(X) that for X = pt assigns to each smooth manifold its Euler characteristic mod 2. The homology theo...
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