Tits alternative for 3-manifold groups
نویسندگان
چکیده
Let M be an irreducible, orientable, closed 3-manifold with fundamental group G. We show that if the pro-p completion Ĝp of G is infinite then G is either soluble-by-finite or contains a free subgroup of rank 2.
منابع مشابه
Tits Alternative in Hypekähler Manifolds
We show an analogous result of the famous Tits alternative for a group G of birational automorphisms of a projective hyperkäher manifold: Either G contains a non-commutative free group or G is an almost abelian group of finite rank. As an application, we show that the automorphism groups of the so-called singular K3 surfaces contain non-commutative free groups.
متن کاملThe Tits Alternative for Tsaranov's Generalized Tetrahedron Groups
A generalized tetrahedron group is defined to be a group admitting the following presentation: 〈x, y, z | x = y = z = W p 1 (x, y) = W q 2 (y, z) = W r 3 (x, z) = 1〉, 2 ≤ l,m, n, p, q, r, where each Wi(a, b) is a cyclically reduced word involving both a and b. These groups appear in many contexts, not least as fundamental groups of certain hyperbolic orbifolds or as subgroups of generalized tri...
متن کاملComplex Hyperbolic Hyperplane Complements
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...
متن کاملThe Tits Alternative for Non-spherical Pride Groups
Pride groups, or “groups given by presentations in which each defining relator involves at most two types of generators”, include Coxeter groups, Artin groups, triangles of groups, and Vinberg’s groups defined by periodic paired relations. We show that every non-spherical Pride group that is not a triangle of groups satisfies the Tits alternative.
متن کاملThe Tits alternative for short generalized tetrahedron groups
A generalized tetrahedron group is defined to be a group admitting the following presentation: 〈x, y, z | xl = ym = zn = W p 1 (x, y) = W q 2 (y, z) = W r 3 (x, z) = 1〉, 2 ≤ l, m, n, p, q, r, where each Wi(a, b) is a cyclically reduced word involving both a and b. These groups appear in many contexts, not least as fundamental groups of certain hyperbolic orbifolds or as subgroups of generalized...
متن کامل