Rigidity and Relative Hyperbolicity of Real Hyperbolic Hyperplane Complements
نویسندگان
چکیده
منابع مشابه
Rigidity and Relative Hyperbolicity of Real Hyperbolic Hyperplane Complements
For n > 3 we study spaces obtained from finite volume complete real hyperbolic n-manifolds by removing a compact totally geodesic submanifold of codimension two. We prove that their fundamental groups are relative hyperbolic, co-Hopf, biautomatic, residually hyperbolic, not Kähler, not isomorphic to lattices in virtually connected real Lie groups, have no nontrivial subgroups with property (T),...
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We study spaces obtained from a complete finite volume complex hyperbolic n-manifold M by removing a compact totally geodesic complex (n−1)-submanifold S . The main result is that the fundamental group of M \S is relatively hyperbolic, relative to fundamental groups of the ends of M \S , and M \S admits a complete finite volume A -regular Riemannian metric of negative sectional curvature. It fo...
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We study the geometry of non-relatively hyperbolic groups. Generalizing a result of Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single peripheral subgroup. This implies that a group being relatively hyperbolic with non-relatively hyperbolic peripheral subgroups is a quasi-isometry invariant...
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The goal of the next two talks is to (1) discuss a class of integrable connections associated to root systems (2) describe their monodromy in terms of quantum groups These connections come in two forms: • Rational form leading to representations of braid groups (this week) • Trigonometric form leading to representations of affine braid groups (next week) The relevance of these connections is th...
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Let G = a 1 ,. .. , a n | a i a j a i · · · = a j a i a j. .. , i < j be an Artin group and let m ij = m ji be the length of each of the sides of the defining relation involving a i and a j. We show if all m ij ≥ 7 then G is relatively hyperbolic in the sense of Farb with respect to the collection of its two-generator subgroups a i , a j for which m ij < ∞.
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2012
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2012.v8.n1.a4