m at h . G T ] 2 9 Ju n 20 09 FOUR - FREE GROUPS AND HYPERBOLIC GEOMETRY MARC
نویسنده
چکیده
We give new information about the geometry of closed, orientable hyperbolic 3-manifolds with 4-free fundamental group. As an application we show that such a manifold has volume greater than 3.44. This is in turn used to show that if M is a closed orientable hyperbolic 3-manifold such that volM ≤ 3.44, then dimZ2 H1(M ;Z2) ≤ 7.
منابع مشابه
ar X iv : m at h / 99 07 13 9 v 1 [ m at h . G T ] 2 2 Ju l 1 99 9 CONSTRUCTING HYPERBOLIC MANIFOLDS
The Coxeter simplex with symbol is a compact hyperbolic 4-simplex and the related Coxeter group Γ is a discrete subgroup of Isom(H 4). The Coxeter simplex with symbol is a spherical 3-simplex, and the related Coxeter group G is the group of symmetries of the regular 120-cell. Using the geometry of the regular 120-cell, Davis [3] constructed an epimorphism Γ → G whose kernel K was torsion-free, ...
متن کاملFour-free Groups and Hyperbolic Geometry
We give new geometric information about the geometry of closed, orientable hyperbolic 3-manifolds with 4-free fundamental group. As an application we show that such a manifold has volume greater than 3.44. This is in turn used to show that if M is a closed orientable hyperbolic 3-manifold such that vol M ≤ 3.44, then dimZ2 H1(M ; Z2) ≤ 7.
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